1) The document discusses methods for visual localization and texture categorization using interest point detection and entropy saliency. It focuses on using scale-space analysis and learning distributions to filter out less salient regions for computational efficiency.
2) An entropy saliency detector is proposed that uses local entropy calculations at multiple scales to identify salient regions. Scale-space analysis allows detection of salient regions without prior knowledge of scale.
3) Techniques including Chernoff information and Kullback-Leibler divergence are discussed for learning distributions of image categories and defining thresholds to filter regions, reducing computational costs of interest point detection and description.
The document summarizes key concepts in image formation, including how light interacts with objects and lenses to form images, and how different imaging systems like the human eye and digital cameras work. It discusses factors that affect image quality such as point spread functions and noise. Methods for analyzing the effects of noise propagation and algorithms on image quality are presented, such as error propagation techniques and Monte Carlo simulations.
Research Inventy : International Journal of Engineering and Science is publis...researchinventy
The document summarizes an improved impulse noise detection and filtering scheme based on an adaptive weighted median filter. The proposed scheme uses an improved impulse noise detector that applies a normalized absolute difference within a filtering window and then removes detected impulse noise using an adaptive switching median filter. Extensive simulation results on standard test images show that the proposed scheme significantly outperforms other median filters in terms of PSNR and MAE for random-valued impulse noise removal. The proposed detection scheme distinguishes noisy and noise-free pixels more efficiently compared to other methods.
Learning Moving Cast Shadows for Foreground Detection (VS 2008)Jia-Bin Huang
The document summarizes a research paper about learning moving cast shadows for foreground detection. It presents a proposed algorithm that uses a confidence-rated Gaussian mixture learning approach and Bayesian framework with Markov random fields to model local and global shadow features. This exploits the complementary nature of local and global features to improve shadow detection. The algorithm is evaluated on outdoor and indoor video sequences, showing improved accuracy over previous methods especially in adaptability to different lighting conditions. Future work could incorporate additional features and more powerful models.
This document discusses error analysis for quasi-Monte Carlo methods. It introduces the trio error identity that decomposes the error into three terms: the variation of the integrand, the discrepancy of the sampling measure from the probability measure, and the alignment between the integrand and the difference between the measures. Several examples are provided to illustrate the identity, including integration over a reproducing kernel Hilbert space. The discrepancy term can be evaluated in O(n^2) operations and converges at different rates depending on the sampling method and properties of the integrand.
A Physical Approach to Moving Cast Shadow Detection (ICASSP 2009)Jia-Bin Huang
This document presents a physical approach to detecting moving cast shadows in video. It introduces a physics-based shadow model that decomposes light sources into direct and ambient components. Color features are used to encode the difference between shadow and background pixels. A weak shadow detector is used to identify shadow candidates, and a Gaussian mixture model learns the shadow model over time. Spatial information is incorporated to improve learning. The approach detects shadows at light/shadow borders separately. Experimental results on various sequences demonstrate improved shadow detection and discrimination rates compared to other methods. Future work will derive physics-based features for a global shadow model and extend the physical model to more complex cases.
Global illumination techniques for the computation of hight quality images in...Frederic Perez
This document appears to be a dissertation defense presentation summarizing work on rendering high quality images accounting for global illumination in general environments, including participating media. The presentation covers global illumination fundamentals, resolution methods for participating media, two first pass methods for solving global illumination, link probabilities for importance sampling, and progressive radiance computation methods. It aims to render high quality images for general scenes potentially including participating media and general optical properties.
The document discusses different perspectives on simulating the mean of a function, including deterministic, randomized, and Bayesian approaches. It summarizes Monte Carlo methods using the central limit theorem and Berry-Esseen inequality to estimate error bounds. Low-discrepancy sampling and cubature methods are described which use Fourier coefficients to bound integration errors. Bayesian cubature is outlined, which assumes the function is drawn from a Gaussian process prior to perform optimal quadrature. Maximum likelihood is used to estimate the kernel hyperparameters.
The document describes various adaptive methods for numerical integration or cubature of functions, including Monte Carlo methods, low-discrepancy sampling, and Bayesian cubature. It discusses approaches to choose sample sizes and weights to guarantee the integral estimate is within a given tolerance of the true integral with high probability. Specific examples discussed include multidimensional Gaussian integrals and estimating Sobol' sensitivity indices.
The document summarizes key concepts in image formation, including how light interacts with objects and lenses to form images, and how different imaging systems like the human eye and digital cameras work. It discusses factors that affect image quality such as point spread functions and noise. Methods for analyzing the effects of noise propagation and algorithms on image quality are presented, such as error propagation techniques and Monte Carlo simulations.
Research Inventy : International Journal of Engineering and Science is publis...researchinventy
The document summarizes an improved impulse noise detection and filtering scheme based on an adaptive weighted median filter. The proposed scheme uses an improved impulse noise detector that applies a normalized absolute difference within a filtering window and then removes detected impulse noise using an adaptive switching median filter. Extensive simulation results on standard test images show that the proposed scheme significantly outperforms other median filters in terms of PSNR and MAE for random-valued impulse noise removal. The proposed detection scheme distinguishes noisy and noise-free pixels more efficiently compared to other methods.
Learning Moving Cast Shadows for Foreground Detection (VS 2008)Jia-Bin Huang
The document summarizes a research paper about learning moving cast shadows for foreground detection. It presents a proposed algorithm that uses a confidence-rated Gaussian mixture learning approach and Bayesian framework with Markov random fields to model local and global shadow features. This exploits the complementary nature of local and global features to improve shadow detection. The algorithm is evaluated on outdoor and indoor video sequences, showing improved accuracy over previous methods especially in adaptability to different lighting conditions. Future work could incorporate additional features and more powerful models.
This document discusses error analysis for quasi-Monte Carlo methods. It introduces the trio error identity that decomposes the error into three terms: the variation of the integrand, the discrepancy of the sampling measure from the probability measure, and the alignment between the integrand and the difference between the measures. Several examples are provided to illustrate the identity, including integration over a reproducing kernel Hilbert space. The discrepancy term can be evaluated in O(n^2) operations and converges at different rates depending on the sampling method and properties of the integrand.
A Physical Approach to Moving Cast Shadow Detection (ICASSP 2009)Jia-Bin Huang
This document presents a physical approach to detecting moving cast shadows in video. It introduces a physics-based shadow model that decomposes light sources into direct and ambient components. Color features are used to encode the difference between shadow and background pixels. A weak shadow detector is used to identify shadow candidates, and a Gaussian mixture model learns the shadow model over time. Spatial information is incorporated to improve learning. The approach detects shadows at light/shadow borders separately. Experimental results on various sequences demonstrate improved shadow detection and discrimination rates compared to other methods. Future work will derive physics-based features for a global shadow model and extend the physical model to more complex cases.
Global illumination techniques for the computation of hight quality images in...Frederic Perez
This document appears to be a dissertation defense presentation summarizing work on rendering high quality images accounting for global illumination in general environments, including participating media. The presentation covers global illumination fundamentals, resolution methods for participating media, two first pass methods for solving global illumination, link probabilities for importance sampling, and progressive radiance computation methods. It aims to render high quality images for general scenes potentially including participating media and general optical properties.
The document discusses different perspectives on simulating the mean of a function, including deterministic, randomized, and Bayesian approaches. It summarizes Monte Carlo methods using the central limit theorem and Berry-Esseen inequality to estimate error bounds. Low-discrepancy sampling and cubature methods are described which use Fourier coefficients to bound integration errors. Bayesian cubature is outlined, which assumes the function is drawn from a Gaussian process prior to perform optimal quadrature. Maximum likelihood is used to estimate the kernel hyperparameters.
The document describes various adaptive methods for numerical integration or cubature of functions, including Monte Carlo methods, low-discrepancy sampling, and Bayesian cubature. It discusses approaches to choose sample sizes and weights to guarantee the integral estimate is within a given tolerance of the true integral with high probability. Specific examples discussed include multidimensional Gaussian integrals and estimating Sobol' sensitivity indices.
The document discusses methods for efficiently and accurately estimating integrals, including Monte Carlo simulation, low-discrepancy sampling, and Bayesian cubature. It notes that product rules for estimating high-dimensional integrals become prohibitively expensive as dimension increases. Adaptive low-discrepancy sampling is proposed as a method that uses Sobol' or lattice points and normally doubles the number of points until a tolerance is reached.
An automated technique for image noise identification using a simple pattern ...Yixin Chen
This document proposes and evaluates a simple technique for identifying image noise types using pattern classification. It involves isolating representative noise samples from a noisy image using filters, extracting statistical features like kurtosis and skewness, and classifying the noise type based on similarity to known noise classes. The technique is tested on images with Gaussian white, uniform white, salt-and-pepper, and speckle noise. Experimental results show the technique can accurately identify single or mixed noise types based on comparing statistical features of isolated noise samples to expected reference values for each noise class.
CVPR2010: Advanced ITinCVPR in a Nutshell: part 4: Isocontours, Registrationzukun
This document discusses using isocontours and image registration. It proposes estimating densities and entropies from isocontour areas rather than samples to allow image-based density estimation without binning issues. The joint probability of two images can be estimated from the overlapping area of isocontours. Mutual information can then be used for registration by minimizing the joint entropy minus individual entropies estimated from isocontour densities. This approach is compared to standard histogramming.
Lesson 26: The Fundamental Theorem of Calculus (Section 021 slides)Matthew Leingang
The document outlines a calculus class lecture on the fundamental theorem of calculus, including recalling the second fundamental theorem, stating the first fundamental theorem, and providing examples of differentiating functions defined by integrals. It gives announcements for upcoming class sections and exam dates, lists the objectives of the current section, and provides an outline of topics to be covered including area as a function, statements and proofs of the theorems, and applications to differentiation.
Wavelet-based Reflection Symmetry Detection via Textural and Color HistogramsMohamed Elawady
This document presents a methodology for wavelet-based reflection symmetry detection using textural and color histograms. It extracts multiscale edge segments using Log-Gabor filters and measures symmetry based on edge orientations, local texture histograms, and color histograms. Evaluation on public datasets shows it outperforms previous methods in detecting single and multiple symmetries, with quantitative and qualitative results presented. Future work could improve the detection using continuous maximal-seeking.
The document summarizes a meeting of the 3rd Thematic Network on photometric stereo estimation from spectral systems. It discusses using photometric stereo techniques to simultaneously recover spectral reflectance and surface relief from images. Specifically, it presents using an RGB digital camera to do this and recover 3D shape and albedo from surfaces under different lighting conditions. Results show good color recovery with around 2% total error between original and simulated images under the same illuminant but different geometries.
Robust edge and corner detection using noise identification and adaptive thre...Yixin Chen
This document presents a two-step method for robust edge and corner detection in noisy images. The first step identifies the type of noise using a pattern classification approach and then restores the image using a suitable denoising filter. Four types of noise are considered: uniform white, Gaussian white, speckle, and salt-and-pepper. Edge and corner strengths are then determined using gradient techniques. Finally, a fuzzy k-means clustering algorithm is used to find adaptive thresholds for detecting edges and corners. Simulation results indicate the proposed algorithm works well.
1. Geodesic sampling and meshing techniques can be used to generate adaptive triangulations and meshes on Riemannian manifolds based on a metric tensor.
2. Anisotropic metrics can be defined to generate meshes adapted to features like edges in images or curvature on surfaces. Triangles will be elongated along strong features to better approximate functions.
3. Farthest point sampling can be used to generate well-spaced point distributions over manifolds according to a metric, which can then be triangulated using geodesic Delaunay refinement.
We will describe and analyze accurate and efficient numerical algorithms to interpolate and approximate the integral of multivariate functions. The algorithms can be applied when we are given the function values at an arbitrary positioned, and usually small, existing sparse set of function values (samples), and additional samples are impossible, or difficult (e.g. expensive) to obtain. The methods are based on local, and global, tensor-product sparse quasi-interpolation methods that are exact for a class of sparse multivariate orthogonal polynomials.
Image segmentation in Digital Image ProcessingDHIVYADEVAKI
Motion is a powerful cue for image segmentation. Spatial motion segmentation involves comparing a reference image to subsequent images to create accumulative difference images (ADIs) that show pixels that differ over time. The positive ADI shows pixels that become brighter over time and can be used to identify and locate moving objects in the reference frame, while the direction and speed of objects can be seen in the absolute and negative ADIs. When backgrounds are non-stationary, the positive ADI can also be used to update the reference image by replacing background pixels that have moved.
This document discusses nanotechnology and its applications to computer circuits. It begins with an overview of nanotechnology, including its history and key concepts. It then discusses various tools used in nanotechnology like electron microscopes. It provides examples of how nanotechnology can be applied to reduce the size of computer circuits. Both benefits like smaller computers and potential disadvantages are mentioned.
The document proposes a weighted Laplacian differences based approach for multispectral anisotropic diffusion for image denoising. It introduces a cross-correlation term between channels to better align edges. The scheme is implemented using split Bregman and tested on color and multispectral images with improvements over existing methods in selective smoothing and utilizing multi-channel information.
IVR - Chapter 2 - Basics of filtering I: Spatial filters (25Mb) Charles Deledalle
Moving averages. Finite differences and edge detectors. Gradient, Sobel and Laplacian. Linear translations invariant filters, cross-correlation and convolution. Adaptive and non-linear filters. Median filters. Morphological filters. Local versus global filters. Sigma filter. Bilateral filter. Patches and non-local means. Applications to image denoising.
The document discusses various techniques for image segmentation including discontinuity-based approaches, similarity-based approaches, thresholding methods, region-based segmentation using region growing and region splitting/merging. Key techniques covered include edge detection using gradient operators, the Hough transform for edge linking, optimal thresholding, and split-and-merge segmentation using quadtrees.
Image Restoration And Reconstruction
Mean Filters
Order-Statistic Filters
Spatial Filtering: Mean Filters
Adaptive Filters
Adaptive Mean Filters
Adaptive Median Filters
CVPR2010: Advanced ITinCVPR in a Nutshell: part 4: additional slideszukun
This document discusses probability density function estimation using isocontours and its applications to image registration and filtering. It proposes estimating densities from image intensities using the areas enclosed by isocontours rather than histograms. This density estimation technique is applied to mutual information-based image registration and anisotropic neighborhood filtering.
On Clustering Financial Time Series - Beyond CorrelationGautier Marti
This document discusses clustering financial time series data using correlation matrices. It summarizes that analyzing 560 credit default swaps over 2500 days, the empirical correlation matrix eigenvalues closely match the theoretical Marchenko-Pastur distribution, indicating noise. Only 26 eigenvalues exceed the theoretical maximum, which may correspond to market and industry factors. Hierarchical clustering can reorder assets to reveal correlation patterns. Filtering by this reveals the underlying network structure. Beyond correlations, copulas represent the dependence structure, and a distance measure is proposed combining L1 and L0 distances of cumulative distribution functions to cluster on full distributions rather than just correlations. Stability tests show the proposed approach yields more robust clusters than standard correlation-based methods.
CVPR2010: Advanced ITinCVPR in a Nutshell: part 3: Feature Selectionzukun
This document discusses high-dimensional feature selection for images, genes, and graphs. It covers several key topics:
1) Feature selection aims to reduce dimensionality for improving classifier performance and identify important patterns. This is challenging with thousands of features.
2) Mutual information is proposed as an optimal criterion for evaluating feature subsets, as it relates to the Bayesian error rate.
3) The mRMR criterion is introduced to maximize feature relevance while minimizing redundancy between features.
The document discusses object recognition and categorization. It outlines the challenges of object recognition including viewpoint variation, illumination changes, occlusion, scale differences, deformations, and background clutter. It also discusses representations, learning methods, and recognition approaches for object categorization including generative vs. discriminative models and different levels of supervision.
CVPR2010: Advanced ITinCVPR in a Nutshell: part 7: Future Trendzukun
The document discusses using wavelet representations for density estimation and shape analysis. It proposes using a constrained maximum likelihood objective to estimate density coefficients in a multi-resolution wavelet basis. Model selection criteria like MDL, AIC and BIC are compared for selecting the number of resolution levels in the wavelet expansion, with MDL shown to be invariant to the multi-resolution analysis used. The criteria are tested on 1D densities with different shapes, with MDL and MSE performing best in distinguishing the densities.
The document discusses methods for efficiently and accurately estimating integrals, including Monte Carlo simulation, low-discrepancy sampling, and Bayesian cubature. It notes that product rules for estimating high-dimensional integrals become prohibitively expensive as dimension increases. Adaptive low-discrepancy sampling is proposed as a method that uses Sobol' or lattice points and normally doubles the number of points until a tolerance is reached.
An automated technique for image noise identification using a simple pattern ...Yixin Chen
This document proposes and evaluates a simple technique for identifying image noise types using pattern classification. It involves isolating representative noise samples from a noisy image using filters, extracting statistical features like kurtosis and skewness, and classifying the noise type based on similarity to known noise classes. The technique is tested on images with Gaussian white, uniform white, salt-and-pepper, and speckle noise. Experimental results show the technique can accurately identify single or mixed noise types based on comparing statistical features of isolated noise samples to expected reference values for each noise class.
CVPR2010: Advanced ITinCVPR in a Nutshell: part 4: Isocontours, Registrationzukun
This document discusses using isocontours and image registration. It proposes estimating densities and entropies from isocontour areas rather than samples to allow image-based density estimation without binning issues. The joint probability of two images can be estimated from the overlapping area of isocontours. Mutual information can then be used for registration by minimizing the joint entropy minus individual entropies estimated from isocontour densities. This approach is compared to standard histogramming.
Lesson 26: The Fundamental Theorem of Calculus (Section 021 slides)Matthew Leingang
The document outlines a calculus class lecture on the fundamental theorem of calculus, including recalling the second fundamental theorem, stating the first fundamental theorem, and providing examples of differentiating functions defined by integrals. It gives announcements for upcoming class sections and exam dates, lists the objectives of the current section, and provides an outline of topics to be covered including area as a function, statements and proofs of the theorems, and applications to differentiation.
Wavelet-based Reflection Symmetry Detection via Textural and Color HistogramsMohamed Elawady
This document presents a methodology for wavelet-based reflection symmetry detection using textural and color histograms. It extracts multiscale edge segments using Log-Gabor filters and measures symmetry based on edge orientations, local texture histograms, and color histograms. Evaluation on public datasets shows it outperforms previous methods in detecting single and multiple symmetries, with quantitative and qualitative results presented. Future work could improve the detection using continuous maximal-seeking.
The document summarizes a meeting of the 3rd Thematic Network on photometric stereo estimation from spectral systems. It discusses using photometric stereo techniques to simultaneously recover spectral reflectance and surface relief from images. Specifically, it presents using an RGB digital camera to do this and recover 3D shape and albedo from surfaces under different lighting conditions. Results show good color recovery with around 2% total error between original and simulated images under the same illuminant but different geometries.
Robust edge and corner detection using noise identification and adaptive thre...Yixin Chen
This document presents a two-step method for robust edge and corner detection in noisy images. The first step identifies the type of noise using a pattern classification approach and then restores the image using a suitable denoising filter. Four types of noise are considered: uniform white, Gaussian white, speckle, and salt-and-pepper. Edge and corner strengths are then determined using gradient techniques. Finally, a fuzzy k-means clustering algorithm is used to find adaptive thresholds for detecting edges and corners. Simulation results indicate the proposed algorithm works well.
1. Geodesic sampling and meshing techniques can be used to generate adaptive triangulations and meshes on Riemannian manifolds based on a metric tensor.
2. Anisotropic metrics can be defined to generate meshes adapted to features like edges in images or curvature on surfaces. Triangles will be elongated along strong features to better approximate functions.
3. Farthest point sampling can be used to generate well-spaced point distributions over manifolds according to a metric, which can then be triangulated using geodesic Delaunay refinement.
We will describe and analyze accurate and efficient numerical algorithms to interpolate and approximate the integral of multivariate functions. The algorithms can be applied when we are given the function values at an arbitrary positioned, and usually small, existing sparse set of function values (samples), and additional samples are impossible, or difficult (e.g. expensive) to obtain. The methods are based on local, and global, tensor-product sparse quasi-interpolation methods that are exact for a class of sparse multivariate orthogonal polynomials.
Image segmentation in Digital Image ProcessingDHIVYADEVAKI
Motion is a powerful cue for image segmentation. Spatial motion segmentation involves comparing a reference image to subsequent images to create accumulative difference images (ADIs) that show pixels that differ over time. The positive ADI shows pixels that become brighter over time and can be used to identify and locate moving objects in the reference frame, while the direction and speed of objects can be seen in the absolute and negative ADIs. When backgrounds are non-stationary, the positive ADI can also be used to update the reference image by replacing background pixels that have moved.
This document discusses nanotechnology and its applications to computer circuits. It begins with an overview of nanotechnology, including its history and key concepts. It then discusses various tools used in nanotechnology like electron microscopes. It provides examples of how nanotechnology can be applied to reduce the size of computer circuits. Both benefits like smaller computers and potential disadvantages are mentioned.
The document proposes a weighted Laplacian differences based approach for multispectral anisotropic diffusion for image denoising. It introduces a cross-correlation term between channels to better align edges. The scheme is implemented using split Bregman and tested on color and multispectral images with improvements over existing methods in selective smoothing and utilizing multi-channel information.
IVR - Chapter 2 - Basics of filtering I: Spatial filters (25Mb) Charles Deledalle
Moving averages. Finite differences and edge detectors. Gradient, Sobel and Laplacian. Linear translations invariant filters, cross-correlation and convolution. Adaptive and non-linear filters. Median filters. Morphological filters. Local versus global filters. Sigma filter. Bilateral filter. Patches and non-local means. Applications to image denoising.
The document discusses various techniques for image segmentation including discontinuity-based approaches, similarity-based approaches, thresholding methods, region-based segmentation using region growing and region splitting/merging. Key techniques covered include edge detection using gradient operators, the Hough transform for edge linking, optimal thresholding, and split-and-merge segmentation using quadtrees.
Image Restoration And Reconstruction
Mean Filters
Order-Statistic Filters
Spatial Filtering: Mean Filters
Adaptive Filters
Adaptive Mean Filters
Adaptive Median Filters
CVPR2010: Advanced ITinCVPR in a Nutshell: part 4: additional slideszukun
This document discusses probability density function estimation using isocontours and its applications to image registration and filtering. It proposes estimating densities from image intensities using the areas enclosed by isocontours rather than histograms. This density estimation technique is applied to mutual information-based image registration and anisotropic neighborhood filtering.
On Clustering Financial Time Series - Beyond CorrelationGautier Marti
This document discusses clustering financial time series data using correlation matrices. It summarizes that analyzing 560 credit default swaps over 2500 days, the empirical correlation matrix eigenvalues closely match the theoretical Marchenko-Pastur distribution, indicating noise. Only 26 eigenvalues exceed the theoretical maximum, which may correspond to market and industry factors. Hierarchical clustering can reorder assets to reveal correlation patterns. Filtering by this reveals the underlying network structure. Beyond correlations, copulas represent the dependence structure, and a distance measure is proposed combining L1 and L0 distances of cumulative distribution functions to cluster on full distributions rather than just correlations. Stability tests show the proposed approach yields more robust clusters than standard correlation-based methods.
CVPR2010: Advanced ITinCVPR in a Nutshell: part 3: Feature Selectionzukun
This document discusses high-dimensional feature selection for images, genes, and graphs. It covers several key topics:
1) Feature selection aims to reduce dimensionality for improving classifier performance and identify important patterns. This is challenging with thousands of features.
2) Mutual information is proposed as an optimal criterion for evaluating feature subsets, as it relates to the Bayesian error rate.
3) The mRMR criterion is introduced to maximize feature relevance while minimizing redundancy between features.
The document discusses object recognition and categorization. It outlines the challenges of object recognition including viewpoint variation, illumination changes, occlusion, scale differences, deformations, and background clutter. It also discusses representations, learning methods, and recognition approaches for object categorization including generative vs. discriminative models and different levels of supervision.
CVPR2010: Advanced ITinCVPR in a Nutshell: part 7: Future Trendzukun
The document discusses using wavelet representations for density estimation and shape analysis. It proposes using a constrained maximum likelihood objective to estimate density coefficients in a multi-resolution wavelet basis. Model selection criteria like MDL, AIC and BIC are compared for selecting the number of resolution levels in the wavelet expansion, with MDL shown to be invariant to the multi-resolution analysis used. The criteria are tested on 1D densities with different shapes, with MDL and MSE performing best in distinguishing the densities.
The document discusses multiclass object detection and how knowledge can be transferred between object categories. It notes that objects share parts and properties, and these commonalities can be leveraged for multitask learning. Models like convolutional neural networks are naturally able to share representations due to translation invariance built into the network. Contextual information from surrounding objects and scenes can also improve detection of difficult objects. Approaches like conditional random fields can model long-range relationships to capture these contextual cues.
- The document contains a table of contents listing applications of image segmentation, including medical image analysis.
- It then discusses using game theory to integrate region-based and boundary-based image segmentation approaches. Pixels and boundaries are modeled as players in a game, with the goal of maximizing both region and boundary posteriors through limited interaction.
- Dominant sets, a graph-based clustering technique, is also discussed for applications like intensity, color, texture segmentation of images and video. Hierarchical segmentation is achieved by regularizing dominant sets with boundary information.
The document discusses the Lucas-Kanade template tracking method for video object tracking. It begins with a review of the Lucas-Kanade optical flow method and how it can be applied to template tracking by imposing the constraint that neighboring pixels within the template have the same flow. It notes the limitation that a constant flow assumption is unreasonable over long periods, but describes how the Lucas-Kanade approach can be generalized to other parametric motion models. It then provides a step-by-step derivation of the Lucas-Kanade tracking algorithm and shows an example using an affine warp model. Finally, it provides an overview of the tracking algorithm and discusses state-of-the-art applications to facial mesh tracking.
Pattern learning and recognition on statistical manifolds: An information-geo...Frank Nielsen
This document provides an overview of Frank Nielsen's talk on pattern learning and recognition using information geometry and statistical manifolds. The talk focuses on departing from vector space representations and dealing with (dis)similarities that do not have Euclidean or metric properties. This poses new theoretical and computational challenges for pattern recognition. The talk describes using exponential family mixture models defined on dually flat statistical manifolds induced by convex functions. On these manifolds, dual coordinate systems and dual affine geodesics allow for computing-friendly representations of divergences and similarities between probabilistic patterns. The techniques aim to achieve statistical invariance and enable algorithmic approaches to problems like Gaussian mixture modeling, shape retrieval, and diffusion tensor imaging analysis.
This document discusses digital image processing concepts including:
- Image acquisition and representation, including sampling and quantization of images. CCD arrays are commonly used in digital cameras to capture images as arrays of pixels.
- A simple image formation model where the intensity of a pixel is a function of illumination and reflectance at that point. Typical ranges of illumination and reflectance are provided.
- Image interpolation techniques like nearest neighbor, bilinear, and bicubic interpolation which are used to increase or decrease the number of pixels in a digital image. Examples of applying these techniques are shown.
- Basic relationships between pixels including adjacency, paths, regions, boundaries, and distance measures like Euclidean, city block, and
Low rank tensor approximation of probability density and characteristic funct...Alexander Litvinenko
This document summarizes a presentation on computing divergences and distances between high-dimensional probability density functions (pdfs) represented using tensor formats. It discusses:
1) Motivating the problem using examples from stochastic PDEs and functional representations of uncertainties.
2) Computing Kullback-Leibler divergence and other divergences when pdfs are not directly available.
3) Representing probability characteristic functions and approximating pdfs using tensor decompositions like CP and TT formats.
4) Numerical examples computing Kullback-Leibler divergence and Hellinger distance between Gaussian and alpha-stable distributions using these tensor approximations.
The document discusses various topics related to raster graphics including:
- How images are displayed on raster graphics systems
- Using output primitives like lines and polygons to describe shapes
- Color models like RGB, CMY, and HSV to represent and describe colors
- Algorithms for line drawing and polygon filling during rasterization
- Techniques for antialiasing like supersampling and area sampling to reduce aliasing artifacts
Slides: A glance at information-geometric signal processingFrank Nielsen
This document discusses information geometry and its applications in statistical signal processing. It introduces several key concepts:
1) Statistical signal processing models data with probability distributions like Gaussians and histograms. Information geometry provides a geometric framework for intuitive reasoning about these statistical models.
2) Exponential family mixture models generalize Gaussian and Rayleigh mixtures and are algorithmically useful in dually flat spaces.
3) Distances between statistical models, like Kullback-Leibler divergence and Bregman divergences, can be interpreted geometrically in terms of convex conjugates and Legendre transformations.
This document provides an introduction to digital image processing. It discusses key topics like image representation as matrices, image digitization which involves sampling and quantization, and the basic steps in digital image processing such as image acquisition, preprocessing, segmentation, feature extraction, recognition and interpretation. Importance of image processing is highlighted for applications like remote sensing, machine vision, and medical imaging. Common techniques like noise filtering, contrast enhancement, compression and their importance are also summarized.
This document discusses Bayesian inference on mixtures models. It covers several key topics:
1. Density approximation and consistency results for mixtures as a way to approximate unknown distributions.
2. The "scarcity phenomenon" where the posterior probabilities of most component allocations in mixture models are zero, concentrating on just a few high probability allocations.
3. Challenges with Bayesian inference for mixtures, including identifiability issues, label switching, and complex combinatorial calculations required to integrate over all possible component allocations.
Computing f-Divergences and Distances of\\ High-Dimensional Probability Densi...Alexander Litvinenko
Talk presented on SIAM IS 2022 conference.
Very often, in the course of uncertainty quantification tasks or
data analysis, one has to deal with high-dimensional random variables (RVs)
(with values in $\Rd$). Just like any other RV,
a high-dimensional RV can be described by its probability density (\pdf) and/or
by the corresponding probability characteristic functions (\pcf),
or a more general representation as
a function of other, known, random variables.
Here the interest is mainly to compute characterisations like the entropy, the Kullback-Leibler, or more general
$f$-divergences. These are all computed from the \pdf, which is often not available directly,
and it is a computational challenge to even represent it in a numerically
feasible fashion in case the dimension $d$ is even moderately large. It
is an even stronger numerical challenge to then actually compute said characterisations
in the high-dimensional case.
In this regard, in order to achieve a computationally feasible task, we propose
to approximate density by a low-rank tensor.
Patch Matching with Polynomial Exponential Families and Projective DivergencesFrank Nielsen
This document presents a method called Polynomial Exponential Family-Patch Matching (PEF-PM) to solve the patch matching problem. PEF-PM models patch colors using polynomial exponential families (PEFs), which are universal smooth positive densities. It estimates PEFs using a Score Matching Estimator and accelerates batch estimation using Summed Area Tables. Patch similarity is measured using a statistical projective divergence called the symmetrized γ-divergence. Experiments show PEF-PM handles noise robustly, symmetries, and outperforms baseline methods.
A MODIFIED DIRECTIONAL WEIGHTED CASCADED-MASK MEDIAN FILTER FOR REMOVAL OF RA...cscpconf
In this paper a Modified Directional Weighted Cascaded-Mask Median (MDWCMM) filter has
been proposed, which is based on three different sized cascaded filtering windows. The
differences between the current pixel and its neighbors aligned with four main directions. A
direction index is used for each edge aligned with a given direction. Then, the minimum of these
four direction indexes is used for impulse detection for each and every masking window.
Depending on the minimum direction indexes among the three windows one window is selected.
The filtering is done on this selected window. Extensive simulations showed that the MDWCMM
filter provides good performances of suppressing impulse with low noise level as well as for highly corrupted images from both gray level and colored benchmarked images.
This document provides a summary of key concepts that must be known for AP Calculus, including:
- Curve sketching and analysis of critical points, local extrema, and points of inflection
- Common differentiation and integration rules like product rule, quotient rule, trapezoidal rule
- Derivatives of trigonometric, exponential, logarithmic, and inverse functions
- Concepts of limits, continuity, intermediate value theorem, mean value theorem, fundamental theorem of calculus
- Techniques for solving problems involving solids of revolution, arc length, parametric equations, polar curves
- Series tests like ratio test and alternating series error bound
- Taylor series approximations and common Maclaurin series
This document summarizes the work completed during a medical physics rotation focused on imaging for treatment planning and verification. Key tasks included:
- Performing quality assurance tests on the electronic portal imaging device (EPID) including measurements of image uniformity, signal-to-noise ratio, and modulation transfer function at varying imaging parameters.
- Analyzing contrast-to-noise ratio, signal-to-noise ratio, and dose dependence using phantoms imaged with the EPID.
- Validating calculations of the EPID's modulation transfer function.
- Ensuring proper alignment of the EPID with the radiation isocenter using reticule alignment tests at different gantry angles.
- Observing clinical treatments for sites
This document discusses sensitometry, which is the quantitative evaluation of how a photographic film responds to radiation and processing. Sensitometry involves producing a sensitometric strip by exposing a film to different levels of radiation and then plotting the characteristic curve. The characteristic curve shows the optical density of the film plotted against the log of relative exposure. Key features of the curve include gross fog, threshold, contrast, latitude, speed/sensitivity and maximum density. Understanding a film's sensitometric properties allows for reproducing an invisible x-ray image with optimal contrast and detail.
The document is a lab manual for a course on Computer Graphics and Multimedia. It contains:
1. A table of contents listing various sections like the time table, university scheme, syllabus, list of books, and list of programs.
2. The time table, university scheme, and syllabus provide details about the course schedule, assessment scheme, and topics to be covered.
3. The list of books and list of programs provide resources for students to refer to for the course and experiments to be performed in the lab.
Variation of peak shape and peak tailing in chromatographymanjikra
This document describes novel finite difference software developed to model chromatographic peak shape when both partition and adsorption control compound distribution on the column. The software uses four dimensionless parameters describing mobile phase fraction, adsorption constant, surface area to volume ratio, and theoretical plates. Variation of these parameters allows simulation of peaks ranging from purely partition-controlled to adsorption-controlled. Results show that at high values of the surface area to volume ratio parameter, adsorption peaks are indistinguishable from partition peaks. This has implications for understanding chromatographic processes. Future work involves developing an expression for retention factor under partition-adsorption conditions.
This document provides an introduction to machine learning, covering key topics such as what machine learning is, common learning algorithms and applications. It discusses linear models, kernel methods, neural networks, decision trees and more. It also addresses challenges in machine learning like balancing fit and robustness, and evaluating model performance using techniques like ROC curves. The goal of machine learning is to build models that can learn from data to make predictions or decisions.
DESPECKLING OF SAR IMAGES BY OPTIMIZING AVERAGED POWER SPECTRAL VALUE IN CURV...ijistjournal
The document describes a novel algorithm for despeckling synthetic aperture radar (SAR) images using particle swarm optimization (PSO) in the curvelet domain. The algorithm first identifies homogeneous regions in the speckled image using variance calculations. It then uses PSO to optimize the thresholding of curvelet coefficients, with the objective of minimizing the average power spectral value. This provides an optimized threshold to apply curvelet-based despeckling. The proposed method is tested on standard images and shown to outperform conventional filters like median and Lee filters in reducing speckle noise.
Similar to CVPR2010: Advanced ITinCVPR in a Nutshell: part 2: Interest Points (20)
Mylyn helps address information overload and context loss when multi-tasking. It integrates tasks into the IDE workflow and uses a degree-of-interest model to monitor user interaction and provide a task-focused UI with features like view filtering, element decoration, automatic folding and content assist ranking. This creates a single view of all tasks that are centrally managed within the IDE.
This document provides an overview of OpenCV, an open source computer vision and machine learning software library. It discusses OpenCV's core functionality for representing images as matrices and directly accessing pixel data. It also covers topics like camera calibration, feature point extraction and matching, and estimating camera pose through techniques like structure from motion and planar homography. Hints are provided for Android developers on required permissions and for planar homography estimation using additional constraints rather than OpenCV's general homography function.
This document provides information about the Computer Vision Laboratory 2012 course at the Institute of Visual Computing. The course focuses on computer vision on mobile devices and will involve 180 hours of project work per person. Students will work in groups of 1-2 people on topics like 3D reconstruction from silhouettes or stereo images on mobile devices. Key dates are provided for submitting a work plan, mid-term presentation, and final report. Contact information is given for the lecturers and teaching assistant.
This document summarizes a presentation on natural image statistics given by Siwei Lyu at the 2009 CIFAR NCAP Summer School. The presentation covered several key topics:
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2) It reviewed common statistical properties found in natural images like 1/f power spectra and non-Gaussian distributions.
3) Maximum entropy and Bayesian models were presented as approaches to model these statistics, with Gaussian and independent component analysis discussed as specific examples.
4) Efficient coding principles from information theory were introduced as a framework for understanding neural representations that aim to decorrelate and
Camera calibration involves determining the internal camera parameters like focal length, image center, distortion, and scaling factors that affect the imaging process. These parameters are important for applications like 3D reconstruction and robotics that require understanding the relationship between 3D world points and their 2D projections in an image. The document describes estimating internal parameters by taking images of a calibration target with known geometry and solving the equations that relate the 3D target points to their 2D image locations. Homogeneous coordinates and projection matrices are used to represent the calibration transformations mathematically.
Brunelli 2008: template matching techniques in computer visionzukun
The document discusses template matching techniques in computer vision. It begins with an overview that defines template matching and discusses some common computer vision tasks it can be used for, like object detection. It then covers topics like detection as hypothesis testing, training and testing techniques, and provides a bibliography.
The HARVEST Programme evaluates feature detectors and descriptors through indirect and direct benchmarks. Indirect benchmarks measure repeatability and matching scores on the affine covariant testbed to evaluate how features persist across transformations. Direct benchmarks evaluate features on image retrieval tasks using the Oxford 5k dataset to measure real-world performance. VLBenchmarks provides software for easily running these benchmarks and reproducing published results. It allows comparing features and selecting the best for a given application.
This document summarizes VLFeat, an open source computer vision library. It provides concise summaries of VLFeat's features, including SIFT, MSER, and other covariant detectors. It also compares VLFeat's performance to other libraries like OpenCV. The document highlights how VLFeat achieves state-of-the-art results in tasks like feature detection, description and matching while maintaining a simple MATLAB interface.
This document summarizes and compares local image descriptors. It begins with an introduction to modern descriptors like SIFT, SURF and DAISY. It then discusses efficient descriptors such as binary descriptors like BRIEF, ORB and BRISK which use comparisons of intensity value pairs. The document concludes with an overview section.
This document discusses various feature detectors used in computer vision. It begins by describing classic detectors such as the Harris detector and Hessian detector that search scale space to find distinguished locations. It then discusses detecting features at multiple scales using the Laplacian of Gaussian and determinant of Hessian. The document also covers affine covariant detectors such as maximally stable extremal regions and affine shape adaptation. It discusses approaches for speeding up detection using approximations like those in SURF and learning to emulate detectors. Finally, it outlines new developments in feature detection.
The document discusses modern feature detection techniques. It provides an introduction and agenda for a talk on advances in feature detectors and descriptors, including improvements since a 2005 paper. It also discusses software suites and benchmarks for feature detection. Several application domains are described, such as wide baseline matching, panoramic image stitching, 3D reconstruction, image search, location recognition, and object tracking.
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This document discusses string algorithms and data structures. It introduces the Knuth-Morris-Pratt algorithm for finding patterns in strings in O(n+m) time where n is the length of the text and m is the length of the pattern. It also discusses common string data structures like tries, suffix trees, and suffix arrays. Suffix trees and suffix arrays store all suffixes of a string and support efficient pattern matching and other string operations in linear time or O(m+logn) time where m is the pattern length and n is the text length.
This document provides a tutorial on how to use Gephi software to analyze and visualize network graphs. It outlines the basic steps of importing a sample graph file, applying layout algorithms to organize the nodes, calculating metrics, detecting communities, filtering the graph, and exporting/saving the results. The tutorial demonstrates features of Gephi including node ranking, partitioning, and interactive visualization of the graph.
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The document discusses the EM algorithm and its application in Probabilistic Latent Semantic Analysis (pLSA). It begins by introducing the parameter estimation problem and comparing frequentist and Bayesian approaches. It then describes the EM algorithm, which iteratively computes lower bounds to the log-likelihood function. Finally, it applies the EM algorithm to pLSA by modeling documents and words as arising from a mixture of latent topics.
This document describes an efficient framework for part-based object recognition using pictorial structures. The framework represents objects as graphs of parts with spatial relationships. It finds the optimal configuration of parts through global minimization using distance transforms, allowing fast computation despite modeling complex spatial relationships between parts. This enables soft detection to handle partial occlusion without early decisions about part locations.
Iccv2011 learning spatiotemporal graphs of human activities zukun
The document presents a new approach for learning spatiotemporal graphs of human activities from weakly supervised video data. The approach uses 2D+t tubes as mid-level features to represent activities as segmentation graphs, with nodes describing tubes and edges describing various relations. A probabilistic graph mixture model is used to model activities, and learning estimates the model parameters and permutation matrices using a structural EM algorithm. The learned models allow recognizing and segmenting activities in new videos through robust least squares inference. Evaluation on benchmark datasets demonstrates the ability to learn characteristic parts of activities and recognize them under weak supervision.
Andreas Schleicher presents PISA 2022 Volume III - Creative Thinking - 18 Jun...EduSkills OECD
Andreas Schleicher, Director of Education and Skills at the OECD presents at the launch of PISA 2022 Volume III - Creative Minds, Creative Schools on 18 June 2024.
Philippine Edukasyong Pantahanan at Pangkabuhayan (EPP) CurriculumMJDuyan
(𝐓𝐋𝐄 𝟏𝟎𝟎) (𝐋𝐞𝐬𝐬𝐨𝐧 𝟏)-𝐏𝐫𝐞𝐥𝐢𝐦𝐬
𝐃𝐢𝐬𝐜𝐮𝐬𝐬 𝐭𝐡𝐞 𝐄𝐏𝐏 𝐂𝐮𝐫𝐫𝐢𝐜𝐮𝐥𝐮𝐦 𝐢𝐧 𝐭𝐡𝐞 𝐏𝐡𝐢𝐥𝐢𝐩𝐩𝐢𝐧𝐞𝐬:
- Understand the goals and objectives of the Edukasyong Pantahanan at Pangkabuhayan (EPP) curriculum, recognizing its importance in fostering practical life skills and values among students. Students will also be able to identify the key components and subjects covered, such as agriculture, home economics, industrial arts, and information and communication technology.
𝐄𝐱𝐩𝐥𝐚𝐢𝐧 𝐭𝐡𝐞 𝐍𝐚𝐭𝐮𝐫𝐞 𝐚𝐧𝐝 𝐒𝐜𝐨𝐩𝐞 𝐨𝐟 𝐚𝐧 𝐄𝐧𝐭𝐫𝐞𝐩𝐫𝐞𝐧𝐞𝐮𝐫:
-Define entrepreneurship, distinguishing it from general business activities by emphasizing its focus on innovation, risk-taking, and value creation. Students will describe the characteristics and traits of successful entrepreneurs, including their roles and responsibilities, and discuss the broader economic and social impacts of entrepreneurial activities on both local and global scales.
Temple of Asclepius in Thrace. Excavation resultsKrassimira Luka
The temple and the sanctuary around were dedicated to Asklepios Zmidrenus. This name has been known since 1875 when an inscription dedicated to him was discovered in Rome. The inscription is dated in 227 AD and was left by soldiers originating from the city of Philippopolis (modern Plovdiv).
Elevate Your Nonprofit's Online Presence_ A Guide to Effective SEO Strategies...TechSoup
Whether you're new to SEO or looking to refine your existing strategies, this webinar will provide you with actionable insights and practical tips to elevate your nonprofit's online presence.
This presentation was provided by Racquel Jemison, Ph.D., Christina MacLaughlin, Ph.D., and Paulomi Majumder. Ph.D., all of the American Chemical Society, for the second session of NISO's 2024 Training Series "DEIA in the Scholarly Landscape." Session Two: 'Expanding Pathways to Publishing Careers,' was held June 13, 2024.
Chapter wise All Notes of First year Basic Civil Engineering.pptxDenish Jangid
Chapter wise All Notes of First year Basic Civil Engineering
Syllabus
Chapter-1
Introduction to objective, scope and outcome the subject
Chapter 2
Introduction: Scope and Specialization of Civil Engineering, Role of civil Engineer in Society, Impact of infrastructural development on economy of country.
Chapter 3
Surveying: Object Principles & Types of Surveying; Site Plans, Plans & Maps; Scales & Unit of different Measurements.
Linear Measurements: Instruments used. Linear Measurement by Tape, Ranging out Survey Lines and overcoming Obstructions; Measurements on sloping ground; Tape corrections, conventional symbols. Angular Measurements: Instruments used; Introduction to Compass Surveying, Bearings and Longitude & Latitude of a Line, Introduction to total station.
Levelling: Instrument used Object of levelling, Methods of levelling in brief, and Contour maps.
Chapter 4
Buildings: Selection of site for Buildings, Layout of Building Plan, Types of buildings, Plinth area, carpet area, floor space index, Introduction to building byelaws, concept of sun light & ventilation. Components of Buildings & their functions, Basic concept of R.C.C., Introduction to types of foundation
Chapter 5
Transportation: Introduction to Transportation Engineering; Traffic and Road Safety: Types and Characteristics of Various Modes of Transportation; Various Road Traffic Signs, Causes of Accidents and Road Safety Measures.
Chapter 6
Environmental Engineering: Environmental Pollution, Environmental Acts and Regulations, Functional Concepts of Ecology, Basics of Species, Biodiversity, Ecosystem, Hydrological Cycle; Chemical Cycles: Carbon, Nitrogen & Phosphorus; Energy Flow in Ecosystems.
Water Pollution: Water Quality standards, Introduction to Treatment & Disposal of Waste Water. Reuse and Saving of Water, Rain Water Harvesting. Solid Waste Management: Classification of Solid Waste, Collection, Transportation and Disposal of Solid. Recycling of Solid Waste: Energy Recovery, Sanitary Landfill, On-Site Sanitation. Air & Noise Pollution: Primary and Secondary air pollutants, Harmful effects of Air Pollution, Control of Air Pollution. . Noise Pollution Harmful Effects of noise pollution, control of noise pollution, Global warming & Climate Change, Ozone depletion, Greenhouse effect
Text Books:
1. Palancharmy, Basic Civil Engineering, McGraw Hill publishers.
2. Satheesh Gopi, Basic Civil Engineering, Pearson Publishers.
3. Ketki Rangwala Dalal, Essentials of Civil Engineering, Charotar Publishing House.
4. BCP, Surveying volume 1
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إضغ بين إيديكم من أقوى الملازم التي صممتها
ملزمة تشريح الجهاز الهيكلي (نظري 3)
💀💀💀💀💀💀💀💀💀💀
تتميز هذهِ الملزمة بعِدة مُميزات :
1- مُترجمة ترجمة تُناسب جميع المستويات
2- تحتوي على 78 رسم توضيحي لكل كلمة موجودة بالملزمة (لكل كلمة !!!!)
#فهم_ماكو_درخ
3- دقة الكتابة والصور عالية جداً جداً جداً
4- هُنالك بعض المعلومات تم توضيحها بشكل تفصيلي جداً (تُعتبر لدى الطالب أو الطالبة بإنها معلومات مُبهمة ومع ذلك تم توضيح هذهِ المعلومات المُبهمة بشكل تفصيلي جداً
5- الملزمة تشرح نفسها ب نفسها بس تكلك تعال اقراني
6- تحتوي الملزمة في اول سلايد على خارطة تتضمن جميع تفرُعات معلومات الجهاز الهيكلي المذكورة في هذهِ الملزمة
واخيراً هذهِ الملزمة حلالٌ عليكم وإتمنى منكم إن تدعولي بالخير والصحة والعافية فقط
كل التوفيق زملائي وزميلاتي ، زميلكم محمد الذهبي 💊💊
🔥🔥🔥🔥🔥🔥🔥🔥🔥
THE SACRIFICE HOW PRO-PALESTINE PROTESTS STUDENTS ARE SACRIFICING TO CHANGE T...indexPub
The recent surge in pro-Palestine student activism has prompted significant responses from universities, ranging from negotiations and divestment commitments to increased transparency about investments in companies supporting the war on Gaza. This activism has led to the cessation of student encampments but also highlighted the substantial sacrifices made by students, including academic disruptions and personal risks. The primary drivers of these protests are poor university administration, lack of transparency, and inadequate communication between officials and students. This study examines the profound emotional, psychological, and professional impacts on students engaged in pro-Palestine protests, focusing on Generation Z's (Gen-Z) activism dynamics. This paper explores the significant sacrifices made by these students and even the professors supporting the pro-Palestine movement, with a focus on recent global movements. Through an in-depth analysis of printed and electronic media, the study examines the impacts of these sacrifices on the academic and personal lives of those involved. The paper highlights examples from various universities, demonstrating student activism's long-term and short-term effects, including disciplinary actions, social backlash, and career implications. The researchers also explore the broader implications of student sacrifices. The findings reveal that these sacrifices are driven by a profound commitment to justice and human rights, and are influenced by the increasing availability of information, peer interactions, and personal convictions. The study also discusses the broader implications of this activism, comparing it to historical precedents and assessing its potential to influence policy and public opinion. The emotional and psychological toll on student activists is significant, but their sense of purpose and community support mitigates some of these challenges. However, the researchers call for acknowledging the broader Impact of these sacrifices on the future global movement of FreePalestine.
A Visual Guide to 1 Samuel | A Tale of Two HeartsSteve Thomason
These slides walk through the story of 1 Samuel. Samuel is the last judge of Israel. The people reject God and want a king. Saul is anointed as the first king, but he is not a good king. David, the shepherd boy is anointed and Saul is envious of him. David shows honor while Saul continues to self destruct.
CVPR2010: Advanced ITinCVPR in a Nutshell: part 2: Interest Points
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Interest Points and Method of Types:
Visual Localization &Texture Categorization
Francisco Escolano
2. Interest Points
Background.From the classical Harris detector, a big bang of
interest-point detectors ensuring some sort of invariance to
zoom/scale, rotation and perspective distortion has emerged since
the proposal of SIFT detector and descriptors [Lowe,04].
These detectors, typically including a multi-scale analysis of the
image, include Harris Affine, MSER [Matas et al,02] and SURF [Bay
et al,08].The need of an intensive comparison of different detectors
(and descriptors) mainly in terms of spatio-temporal stability
(repeatability, distinctiveness and robustness) is yet a classic
challenge [Mikolajczyk et al, 05].
Stability experiments are key to predict the future behavior of the
dectector/descriptor in subsequent tasks (bag-of-words recognition,
matching,...)
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3. Entropy Saliency Detector
Local Saliency, in contrast to global one [Ullman, 96], means local
distinctiveness (outstanding/popout pixel distributions over the
image) [Julesz,81][Nothdurft,00].
In Computer Vision, a mild IT definition of local saliency is linked to
visual unpredictability [Kadir and Brady,01]. Then a salient region is
locally unpredictible (measured by entropy) and this is consistent
with a peak of entropy in scale-space.
Scale-space analysis is key because we do not know the scale of
regions beforehand. In addition, isotropic detections may be
extended to affine detectors with an extra computational cost. (see
Alg. 1).
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4. Entropy Saliency Detector(2)
Alg. 1: Kadir and Brady scale saliency algorithm
Input: Input image I, initial scale smin , final scale smax
for each pixel x do
for each scale s between smin and smax do
L
Calculate local entropy HD (s, x) = − Ps,x (di ) log2 Ps,x (di )
i=1
end
Choose the set of scales at which entropy is a local maximum
Sp = {s : HD (s − 1, x) < HD (s, x) > HD (s + 1, x)}
for each scale s between smin and smax do
if s ∈ Sp then
Entropy weight calculation by means of a self-dissimilarity measure in scale space
s 2 L
WD (s, x) = 2s−1 i=1 | Ps,x (di ) − Ps−1,x (di ) |
Entropy weighting YD (s, x) = HD (s, x)WD (s, x)
end
end
end
Output: A disperse three dimensional matrix containing weighted local entropies for all pixels at those scales where
entropy is peaked
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6. Learning and Chernoff Information
Scale-space analysis, is, thus, one of the bottlenecks of the process.
However, having a prior knowledge of the statistics of the images
being analyzed it is possible to discard a significant number of
pixels, and thus, avoid scale-space analysis.
Working hypothesis
If the local distribution around a pixel at a scale smax is highly
homogeneous (low entropy) one may assume that for scales
s < smax it will happen the same. Thus, scale-space peaks will not
exist in this range of scales.[Suau and Escolano,08].
Inspired in statistical detection of edges [Konishi et al.,03] and
contours [Cazorla & Escolano, 03] and also in contour grouping
[Cazorla et al.,02].
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7. Learning and Chernoff Information(2)
Relative entropy and threshold, a basic procedure consists of
computing the ratio between the entropy at smax and the maximum
of entropies for all pixels at their smax
Filtering by homogeneity along scale-space
1. Calculate the local entropy HD for each pixel at scale smax .
2. Select an entropy threshold σ ∈ [0, 1].
HD (x,smax )
3. X = {x | maxx {HD (x,smax )} > σ}
4. Apply scale saliency algorithm only to those pixels x ∈ X .
What is the optimal threshold σ?
7/32
8. Learning and Chernoff Information(3)
Images belonging to the same image category or environment share
similar intensity and texture distributions, so it seems reasonable to
think that the entropy values of their most salient regions will lay in
the same range.
On/Off distributions
The pon (θ) defines the probability of a region to be part of the most
salient regions of the image given that its relative entropy value is θ,
while poff (θ) defines the probability of a region to do not be part of
the most salient regions of the image.
Then, the maximum relative entropy σ being pon (σ) > 0 may be
choosen as an entropy threshold for that image category by finding a
trade-off between false positives and negatives.
8/32
9. Learning and Chernoff Information (4)
Figure: On(blue)/Off(red) distributions and thresholds.
9/32
10. Learning and Chernoff Information (5)
Chernoff Information
The expected error rate of a likelihood test based on pon (φ) and
poff (φ) decreases exponentially with respect to C (pon (φ), poff (φ)),
where:
J
C (p, q) = − min log p λ (yj )q 1−λ (yj )
0≤λ≤1
j=1
A related measure is Bhattachryya Distance (Chernoff with
λ = 1/2):
J
1 1
BC (p, q) = − log p 2 (yj )q 2 (yj )
j=1
10/32
11. Learning and Chernoff Information (6)
Chernoff Bounds
A threshold T must be chosen for an image class so any pixel from
an image belonging to the same image class may be discarded if
log(pon (θ)/poff (θ)) < T . Being T
−D(poff (θ)||pon (θ)) < T < D(pon (θ)||poff (θ))
and D(.||.) the Kullback-Leibler divergence:
J
p(yj )
D(p||q) = p(yj ) log
q(yj )
j=1
11/32
12. Learning and Chernoff Information (7)
Figure: Filtering for different image categories, T = 0
12/32
14. Learning and Chernoff Information (9)
Figure: Filtering in the Caltech101 database, T = Tmin vs T = 0
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15. Learning and Chernoff Information (10)
Chernoff & Classification Error
Following the Chernoff theorem which exploits the Sanov’s theorem
(quantifying probability of rare events), for n i.i.d. samples
distributed by following Q, the probability of error for the test with
hypotheses Q = pon and Q = poff is given by:
pe = πon 2−nD(pλ ||pon ) + πoff 2−nD(pλ ||poff )
= 2−n min{D(pλ ||pon ),D(pλ ||poff )} ,
being πon and πoff the priors.
Choosing λ so that D(pλ ||pon ) = D(pλ ||poff ) = C (pon , poff ) we
have that Chernoff information is the best achievable exponent in
the Bayesian probability of error.
15/32
16. Coarse-to-fine Visual Localization
Problem Statement
A 6DOF SLAM method has built a 3D+2D map of an
indoor/outdoor environment [Lozano et al, 09].
We have manually marked 6 environments and trained a
minimal complexity supervised classifier (see next lesson) for
performing coarse localization.
We got the statistics from the images of each environment in
order to infer their respective pon and poff distributions and
hence their Chernoff information and T bounds.
Once a test image is submitted it is classified and filtered
according to Chernoff information. Then the keypoints are
computed.
16/32
17. Coarse-to-fine Visual Localization (2)
Problem Statement (cont)
Using the SIFT descriptors of the keypoints and the GTM
algorithm [Aguilar et al, 09] we match the image with a
structural + appearance prototype previously unsupervisedly
learned through an EM-algorithm.
The prototype tells us what is the sub-environment to which
the image belongs.
In order to perform fine localization we match the image with
the structure and appearance off all images assigned to a given
sub-enviromnent and then select the one with highest
likelihood.
See more in the Feature-selection lesson.
17/32
20. KD-Partitions and Entropy
Data Partitions and Density Estimation
Let X be a d-dimensional random variable, and f (x) its pdf. Let
A = {Aj |j = 1, . . . , m} be a partition of X for which Ai ∩ Aj = ∅ if
i = j and j Aj = X . Then, we have [Stowell& Plumbley, 09]:
Aj f (x) nj
fAj = ˆ
fAj (x) = ,
µ(Aj ) nµ(Aj )
where fAj approximates f (x) in each cell, µ(Aj ) is the d-dimensional
volume of Aj . If f (x) is unknown and we are given a set of samples
X = {x1 , . . . , xn } from it, being xi ∈ Rd , we can approximate the
probability of f (x) in each cell as pj = nj /n, where nj is the number
of samples in cell Aj .
20/32
21. KD-Partitions and Entropy
Entropy Estimation
Differential Shannon entropy is then asymptotically approximated by
m
ˆ nj n
H= log µ(Aj ) ,
n nj
j=1
and such approximation relies on the way of building the partition.
It is created recursively following the data splitting method of the
k-d tree algorithm. At each level, data is split at the median along
one axis. Then, data splitting is recursively applied to each subspace
until an uniformity stop criterion is satisfied.
21/32
22. KD-Partitions and Entropy
Entropy Estimation (cont)
The aim of this stop criterion is to ensure that there is an uniform
density in each cell in order to best approximate f (x). The chosen
uniformity test is fast and depends on the median. The distribution
of the median of the samples in Aj tends to a normal distribution
that can be standardized as:
√ 2medd (Aj ) − mind (Aj ) − maxd (Aj )
Zj = nj ,
maxd (Aj ) − mind (Aj )
When |Zj | > 1.96 (the 95% confidence threshold of a standard
Gaussian) declare significant deviation from uniformity. Not applied
√
until there are less than n data points in each partition.
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23. KD-Partitions and Divergence
KDP Total-Variation Divergence
The total variation distance [Denuit and Bellegem,01] between two
probability measures P and Q for a finite alphabet, is given by:
1
δ(P, Q) = |P(x) − Q(x)| .
2 x
Then, the divergence is simply formulated as:
p
1 nx,j no,j
δ(P, Q) = |pj −qj | ∈ [0, 1], p(Aj ) = = pj p(Aj ) = = qj
2 nx no
j=1
where pi and pj are the proportion of samples of P and Q in cell Aj .
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25. Multi-Dimensional Saliency Algorithm
Alg. 2: MD Kadir and Brady scale saliency algorithm
Input: m−dimensional image I , initial scale smin , final scale smax
for each pixel x do
for each scale si between smin and smax do
(1) Create a m−dimensional sample set Xi = {xi } from N (si , x) in image I ;
(2) Apply kd-partition to X in order to estimate
m
nj n
ˆ
H(si , x) = − log µ(Aj )
j=1
n nj
if i > smin + 1 then
ˆ ˆ ˆ
(3)if H(si−2 , x) < H(si−1 , x) > H(si , x) then
r
1
(4)Compute Divergence: W = δ(Xi−1 , Xi−2 ) = 2 |pi−1 − pi−2 |
j=1
ˆ
(5)Entropy weighting Y (si−1 , x) = H(si−1 , x) · W
end
else
(6) Y (si−1 , x) = 0
end
end
end
end
Output: An array Y containing weighted entropy values for all pixels on image at each scale
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26. MD-(Gabor) Saliency for Textures
KDP Total-Variation Divergence
Use Brodatz dataset (111 textures and 9 images per category:
999 images).
Use 15 Gabor filters for obtaining multi-dimensional data.
Both graylevel saliency and MD saliency are tuned to obtain
150 salient points.
Use each image in the database as query image.
Use: saliency with only RIFT, only spin images, and combining
RIFT and spin images.
retrieval-recall results strongly influenced by the type of
descriptor used [Suau & Escolano,10].
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27. MD-(Gabor) Saliency for Textures (2)
Figure: Salient pixels in textures. Left: MD-KPD. Right: Graylevel saliency
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29. References
[Lowe,04] Lowe, D. (2004). Distinctive image features from scale
invariant keypoints. International Journal of Computer Vision,
60(2):91–110
[Matas et al,02] Matas, J., Chum, O., Urban, M., and Pajdla, T.
(2004). Ro- bust wide baseline stereo from maximally stable extremal
regions. Image and Vision Computing, 22(10):761–767
[Mikolajczyk et al, 05] Mikolajczyk, K., Tuytelaars, T., Schmid, C.,
Zisserman, A., Matas, J., Schaffalitzky, F., Kadir, T., and Gool, L. V.
(2005). A comparison of afne region detectors. International Journal
of Computer Vision, 65(1/2):43–72
[Ullman,96] High-level Vision, MIT Press, 1996
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30. References (2)
[Julesz,81] Julesz, B. (1981). Textons, the Elements of Texture
Perception, and their Interactions. Nature 290 (5802): 91–97
[Nothdurft,00] Nothdurft, H.C. Salience from feature contrast:
variations with texture density. Vision Research 40 (2000): 3181–3200
[Kadir and Brady,01] Kadir, T. and Brady, M. (2001). Scale, saliency
and image description. International Journal of Computer Vision,
45(2):83–105
[Suau and Escolano,08] Suau, P., Escolano, F. (2008) Bayesian
Optimization of the Scale Saliency Filter. Image and Vision
Computing, 26(9), pp. 1207–1218
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31. References (3)
[Konishi et al.,03] Konishi, S., Yuille, A. L., Coughlan, J. M., and
Zhu, S. C. (2003). Statistical edge detection: learning and evaluating
edge cues. IEEE Trans. on PAMI, 25(1):57–74
[Cazorla & Escolano] Cazorla, M. and Escolano, F. (2003). Two
Bayesian methods for junction detection. IEEE Transactions on
Image Processing, 12(3):317–327
[Cazorla et al.,02] Cazorla, M., Escolano, F., Gallardo, D., and Rizo,
R. (2002). Junction detection and grouping with probabilistic edge
models and Bayesian A*. Pattern Recognition, 35(9):1869–1881
[Lozano et al, 09] Lozano M,A., Escolano, F., Bonev, B., Suau, P.,
Aguilar, W., S´ez, J.M., Cazorla, M. (2009). Region and constell.
a
based categorization of images with unsupervised graph learning.
Image Vision Comput. 27(7): 960–978
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32. References (4)
[Aguilar et al, 09] Aguilar, W., Frauel Y., Escolano, F., Martnez-Prez,
M.E., Espinosa-Romero, A., Lozano, M.A. (2009) A robust Graph
Transformation Matching for non-rigid registration. Image Vision
Comput. 27(7): 897–910
[Stowell& Plumbley, 09] Stowell, D. and Plumbley, M. D. (2009).
Fast multidimensional entropy estimation by k-d partitioning. IEEE
Signal Processing Letters, 16(6):537–540
[Suau & Escolano,10] Suau, P., Escolano, F. (2010). Analysis of the
Multi-Dimensional Scale Saliency Algorithm and its Application to
Texture Categorization, SSPR’2010 (accepted)
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