The document provides an overview of a 3-view camera self-calibration and 3D reconstruction algorithm. It begins with feature detection in each image, associates features across the 3 views to estimate the trifocal tensor using RANSAC. This is used to compute compatible projective camera matrices and rectify them to metric cameras. An initial 3D point cloud is constructed and refined through bundle adjustment. The algorithm aims to estimate the camera's intrinsic parameters and reconstruct the 3D scene from three uncalibrated images without calibration targets.
Intelligent Image Enhancement and Restoration - From Prior Driven Model to Ad...Wanjin Yu
ICME2019 Tutorial: Intelligent Image Enhancement and Restoration - From Prior Driven Model to Advanced Deep Learning Part 4: retinex model based low light enhancement
Image segmentation refers to partitioning a digital image into multiple regions or sets of pixels based on characteristics like color or texture. The goal is to simplify the image representation to make it easier to analyze. Some applications in medical imaging include locating tumors, measuring tissue volumes, and computer-guided surgery. Common segmentation techniques include thresholding, edge detection, region growing, and split-and-merge approaches.
Three key points about structure from motion:
1. Given multiple images of 3D points, structure from motion aims to estimate the 3D structure and camera motion from 2D point correspondences across images.
2. For affine cameras, factorization methods can be used to decompose the measurement matrix and obtain the motion and structure matrices up to an affine ambiguity.
3. For projective cameras, an iterative procedure alternates between factorization to estimate motion/structure and re-solving for depths to handle the projective ambiguity. At least 7 point correspondences are needed for a two-camera case.
Structure and Motion - 3D Reconstruction of Cameras and StructureGiovanni Murru
The document discusses structure from motion reconstruction from multiple images. It provides an overview of the steps to:
1. Estimate camera motion and 3D structure from a sequence of images using a stratified approach, starting with projective reconstruction and refining to affine and metric reconstruction.
2. Reconstruct structure and motion for two datasets - a public dataset and a personal dataset acquired by the student.
3. The key steps are feature detection, matching, estimating the fundamental matrix, triangulating 3D points, identifying the plane at infinity to upgrade from projective to affine reconstruction, and further refinement to metric reconstruction if possible.
This document summarizes a student project on face recognition. It begins with an introduction to face recognition, its applications, and common challenges. It then reviews literature on existing face recognition methods and identifies problems related to tilted poses and variations in illumination and expression. The proposed method will work to improve recognition rates under these conditions in two phases - training and testing. The method aims to enhance the preprocessing and feature extraction steps to make the system more robust. A basic flowchart of the proposed approach is provided, and the document concludes with references.
The document discusses two-view geometry in computer vision. It introduces epipolar geometry and how corresponding points in two images are related by the fundamental matrix. It describes how the fundamental matrix can be estimated from point correspondences using the 8-point algorithm and its normalized variant to improve robustness. The document also briefly mentions that multi-view geometry for three or more views is described by higher order tensors like the trifocal and quadrifocal tensors.
Two cameras displaced horizontally from one another can obtain two differing views of a scene, similar to human binocular vision. By comparing these two images and examining the relative positions of objects, 3D information like depth can be extracted from the 2D images. This process is called stereo vision. The depth information is contained in pixel displacements between the two images called disparities, which are inversely proportional to distance. Knowing camera intrinsics and their relative pose allows reconstructing 3D point positions through triangulating corresponding image points. Reconstruction accuracy depends on factors like disparity, baseline distance, and focal length.
Intelligent Image Enhancement and Restoration - From Prior Driven Model to Ad...Wanjin Yu
ICME2019 Tutorial: Intelligent Image Enhancement and Restoration - From Prior Driven Model to Advanced Deep Learning Part 4: retinex model based low light enhancement
Image segmentation refers to partitioning a digital image into multiple regions or sets of pixels based on characteristics like color or texture. The goal is to simplify the image representation to make it easier to analyze. Some applications in medical imaging include locating tumors, measuring tissue volumes, and computer-guided surgery. Common segmentation techniques include thresholding, edge detection, region growing, and split-and-merge approaches.
Three key points about structure from motion:
1. Given multiple images of 3D points, structure from motion aims to estimate the 3D structure and camera motion from 2D point correspondences across images.
2. For affine cameras, factorization methods can be used to decompose the measurement matrix and obtain the motion and structure matrices up to an affine ambiguity.
3. For projective cameras, an iterative procedure alternates between factorization to estimate motion/structure and re-solving for depths to handle the projective ambiguity. At least 7 point correspondences are needed for a two-camera case.
Structure and Motion - 3D Reconstruction of Cameras and StructureGiovanni Murru
The document discusses structure from motion reconstruction from multiple images. It provides an overview of the steps to:
1. Estimate camera motion and 3D structure from a sequence of images using a stratified approach, starting with projective reconstruction and refining to affine and metric reconstruction.
2. Reconstruct structure and motion for two datasets - a public dataset and a personal dataset acquired by the student.
3. The key steps are feature detection, matching, estimating the fundamental matrix, triangulating 3D points, identifying the plane at infinity to upgrade from projective to affine reconstruction, and further refinement to metric reconstruction if possible.
This document summarizes a student project on face recognition. It begins with an introduction to face recognition, its applications, and common challenges. It then reviews literature on existing face recognition methods and identifies problems related to tilted poses and variations in illumination and expression. The proposed method will work to improve recognition rates under these conditions in two phases - training and testing. The method aims to enhance the preprocessing and feature extraction steps to make the system more robust. A basic flowchart of the proposed approach is provided, and the document concludes with references.
The document discusses two-view geometry in computer vision. It introduces epipolar geometry and how corresponding points in two images are related by the fundamental matrix. It describes how the fundamental matrix can be estimated from point correspondences using the 8-point algorithm and its normalized variant to improve robustness. The document also briefly mentions that multi-view geometry for three or more views is described by higher order tensors like the trifocal and quadrifocal tensors.
Two cameras displaced horizontally from one another can obtain two differing views of a scene, similar to human binocular vision. By comparing these two images and examining the relative positions of objects, 3D information like depth can be extracted from the 2D images. This process is called stereo vision. The depth information is contained in pixel displacements between the two images called disparities, which are inversely proportional to distance. Knowing camera intrinsics and their relative pose allows reconstructing 3D point positions through triangulating corresponding image points. Reconstruction accuracy depends on factors like disparity, baseline distance, and focal length.
Depth Fusion from RGB and Depth Sensors IIYu Huang
This document outlines several methods for fusing depth information from RGB and depth sensors. It begins with an outline listing 14 different depth fusion techniques. It then provides more detailed descriptions of several methods:
1. A noise-aware filter is proposed for real-time depth upsampling that takes into account inherent noise in real-time depth data.
2. Integrating LIDAR into stereo disparity computation to reduce false positives and increase density in textureless regions.
3. A probabilistic fusion method combines sparse LIDAR and dense stereo to provide accurate dense depth maps and uncertainty estimates in real-time.
4. A LIDAR-guided approach generates monocular stixels, supporting more efficient
Noise2Score: Tweedie’s Approach to Self-Supervised Image Denoising without Cl...KwanyoungKim7
This document presents Noise2Score, a unified framework for self-supervised image denoising without clean images. It discusses how previous approaches like Noise2Noise, SURE, and supervised learning are special cases of Tweedie's formula for the exponential family. Noise2Score estimates the score function using an amortized residual denoising autoencoder, allowing it to denoise images with different noise models like Gaussian, Poisson, and Gamma noise, using the same network training. The framework provides a novel unified approach for self-supervised image denoising without requiring paired clean-noisy images.
Lec12: Shape Models and Medical Image SegmentationUlaş Bağcı
ShapeModeling – M-reps
– Active Shape Models (ASM)
– Oriented Active Shape Models (OASM)
– Application in anatomy recognition and segmentation – Comparison of ASM and OASM
ActiveContour(Snake) • LevelSet • Applications Enhancement, Noise Reduction, and Signal Processing • MedicalImageRegistration • MedicalImageSegmentation • MedicalImageVisualization • Machine Learning in Medical Imaging • Shape Modeling/Analysis of Medical Images Deep Learning in Radiology Fuzzy Connectivity (FC) – Affinity functions • Absolute FC • Relative FC (and Iterative Relative FC) • Successful example applications of FC in medical imaging • Segmentation of Airway and Airway Walls using RFC based method Energy functional – Data and Smoothness terms • GraphCut – Min cut – Max Flow • ApplicationsinRadiologyImages
Template matching is a technique used to classify objects by comparing portions of images against templates. It involves moving a template image across a larger source image to find the best match based on pixel-by-pixel comparisons of brightness levels. For gray-level images, the difference in brightness levels at each pixel location is used rather than a simple yes/no match. Template matching is commonly used to identify simple objects like printed characters. Matlab examples demonstrate template matching on sample data sets and correlation maps show the strength of matches across the source images.
NeRF: Representing Scenes as Neural Radiance Fields for View Synthesis taeseon ryu
해당 논문은 3D Aware 모델입니다 StyleGAN 같은 경우에는 어떤 하나의 피처에 대해서 Editing 하고 싶을 때 입력에 해당하는 레이턴트 백터를 찾아서 레이턴트 백터를 수정함으로써 입에 해당하는 피쳐를 바꿀 수 있었는데 이런 컨셉을 그대로 착안해서
GAN 스페이스 논문에서는 인풋이 들어왔을 때 어떤 공간적인 정보까지도 에디팅하려고 시도했습니다 결과를 봤을 때 로테이션 정보가 어느 정도 잘 학습된 것 같지만 같은 사람이 아닌 것 같이 인식되기도 합니다 이러한 문제를 이제 disentangle 되지 않았다라고 하는 게 원하는 피처만 변화시켜야 되는 것과 달리 다른 피처까지도 모두 학습 모두 변했다는 것인데 이를 좀 더 효율적으로 3D를 더 잘 이해시키기 위해서 탄생한 논문입니다.
This document presents a methodology for motion blur image restoration using an alternating direction balanced regularization filter. It begins with an introduction discussing image restoration and types of image degradation like blur and noise. It then discusses a literature review of existing techniques for motion blur parameter estimation and image restoration. The proposed methodology is described as estimating the motion blur angle and length using Gabor filters and radial basis functions, then restoring the image using an alternating direction balanced regularization filter. Experimental results on various standard test images are provided, comparing the proposed method to existing techniques based on metrics like PSNR and MSE. The conclusions discuss that the proposed method provides improved restoration quality over existing methods.
Presentation for the Berlin Computer Vision Group, December 2020 on deep learning methods for image segmentation: Instance segmentation, semantic segmentation, and panoptic segmentation.
This document discusses camera models and image formation. It begins by describing the pinhole camera model and how a pinhole creates an image by blocking most light rays. A lens is then introduced to focus light rays onto film. Projection using the pinhole camera is modeled mathematically using homogeneous coordinates. Perspective projection is introduced, along with the camera projection matrix which models the camera's intrinsics and extrinsics. Distortion effects like radial distortion are also covered.
The document discusses sources of distortion in underwater images such as light scattering and color change. It proposes a method called Wavelength Compensation and Dehazing (WCID) to enhance underwater image visibility and color fidelity. WCID uses a hazy image formation model and dark channel prior to estimate depth maps and remove haze. It can also detect and remove effects of artificial light sources. The method is shown to outperform other dehazing techniques in experiments by achieving higher signal-to-noise ratios and more robust performance at different water depths.
The document describes a vehicle detection system using a fully convolutional regression network (FCRN). The FCRN is trained on patches from aerial images to predict a density map indicating vehicle locations. The proposed system is evaluated on two public datasets and achieves higher precision and recall than comparative shallow and deep learning methods for vehicle detection in aerial images. The system could help with applications like urban planning and traffic management.
An introduction to image processing in addition to explaining the concept of group operations.
Find me on:
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Google Scholar
https://scholar.google.com.eg/citations?user=r07tjocAAAAJ&hl=en
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https://www.mendeley.com/profiles/ahmed-gad12/
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https://orcid.org/0000-0003-1978-8574
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http://stackoverflow.com/users/5426539/ahmed-gad
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Los anaglifos fueron inventados en 1853 y permiten ver imágenes en 3D usando gafas especiales. En 1891 se realizaron las primeras proyecciones públicas con este método. En 1955 se inventó en España el sistema estereocrom que permitía anaglifos en color. En 1950 Ariznavarreta creó diapositivas anaglíficas en color y en 1954 publicó cromos anaglíficos de películas. Los anaglifos usan filtros de colores complementarios como rojo y cian para que cada ojo vea una imagen diferente y el
This document provides an overview of image enhancement techniques. It discusses the objectives of image enhancement, which is to process an image to make it more suitable for a specific application or task. The document focuses on spatial domain techniques for image enhancement, specifically point processing methods and histogram processing. It categorizes image enhancement methods into two broad categories: spatial domain methods, which directly manipulate pixel values; and frequency domain methods, which first convert the image into the frequency domain before performing enhancements.
The document discusses decision trees and random forests for machine learning. It begins with an overview and historical perspective on decision trees and random forests. It then describes how a decision tree is formed by splitting nodes based on features and assessing purity. Random forests grow multiple decision trees on bootstrapped data samples and aggregate their predictions. The document discusses applications in areas like computer vision, medical imaging, and engineering design. It covers computational complexity and variable importance analysis. Finally, it discusses current research challenges and opportunities in decision tree and random forest algorithms and architectures.
Automated attendance system based on facial recognitionDhanush Kasargod
A MATLAB based system to take attendance in a classroom automatically using a camera. This project was carried out as a final year project in our Electronics and Communications Engineering course. The entire MATLAB code I've uploaded it in mathworks.com. Also the entire report will be available at academia.edu page. Will be delighted to hear from you.
The document discusses various image enhancement techniques in Matlab, including filtering, predefined filters, image enhancement tools, image restoration, dilation/erosion functions, and dithering. Filtering can be used to modify images through operations like smoothing, sharpening, and edge enhancement. Predefined filters like 'gaussian' and 'laplacian' can be applied to images with functions like fspecial and imfilter. Additional tools for operations such as histogram equalization, noise addition, and filtering are also covered.
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.
The document discusses content-based image retrieval (CBIR). It provides a brief history of CBIR, noting it originated in 1992. It describes challenges of CBIR, including the semantic gap between low-level features extracted and high-level human concepts. It also outlines common CBIR techniques like color, shape, and texture analysis. Applications are described as image search and browsing. Limitations include not fully capturing human visual understanding.
This thesis presents research on using deep learning methods for feature extraction from satellite imagery to identify landslide pixels. The objectives are to classify land cover using machine learning algorithms like SVM and random forests in Google Earth Engine, design and evaluate a deep neural network for landslide identification, and compare performance of deep learning models in MATLAB. Results show that a neural network achieved over 98% accuracy at identifying landslide pixels. Future work proposes developing new indices for improved identification and an automatic landslide monitoring platform.
3D Reconstruction from Multiple uncalibrated 2D Images of an ObjectAnkur Tyagi
3D reconstruction is the process of capturing the shape and appearance of real objects. In this project we are using passive methods which only use sensors to measure the radiance reflected or emitted by the objects surface to infer its 3D structure.
This document summarizes a research paper that proposes a novel background removal algorithm using fuzzy c-means clustering. It begins by introducing background subtraction and some of the challenges. It then describes the proposed algorithm which uses edge detection to locate regions of interest before applying fuzzy c-means clustering to segment the foreground object. The algorithm achieves significant computation time reduction compared to other methods. Experimental results show the proposed method has higher true positive rates and accuracy compared to other algorithms, though precision and similarity are slightly lower.
Depth Fusion from RGB and Depth Sensors IIYu Huang
This document outlines several methods for fusing depth information from RGB and depth sensors. It begins with an outline listing 14 different depth fusion techniques. It then provides more detailed descriptions of several methods:
1. A noise-aware filter is proposed for real-time depth upsampling that takes into account inherent noise in real-time depth data.
2. Integrating LIDAR into stereo disparity computation to reduce false positives and increase density in textureless regions.
3. A probabilistic fusion method combines sparse LIDAR and dense stereo to provide accurate dense depth maps and uncertainty estimates in real-time.
4. A LIDAR-guided approach generates monocular stixels, supporting more efficient
Noise2Score: Tweedie’s Approach to Self-Supervised Image Denoising without Cl...KwanyoungKim7
This document presents Noise2Score, a unified framework for self-supervised image denoising without clean images. It discusses how previous approaches like Noise2Noise, SURE, and supervised learning are special cases of Tweedie's formula for the exponential family. Noise2Score estimates the score function using an amortized residual denoising autoencoder, allowing it to denoise images with different noise models like Gaussian, Poisson, and Gamma noise, using the same network training. The framework provides a novel unified approach for self-supervised image denoising without requiring paired clean-noisy images.
Lec12: Shape Models and Medical Image SegmentationUlaş Bağcı
ShapeModeling – M-reps
– Active Shape Models (ASM)
– Oriented Active Shape Models (OASM)
– Application in anatomy recognition and segmentation – Comparison of ASM and OASM
ActiveContour(Snake) • LevelSet • Applications Enhancement, Noise Reduction, and Signal Processing • MedicalImageRegistration • MedicalImageSegmentation • MedicalImageVisualization • Machine Learning in Medical Imaging • Shape Modeling/Analysis of Medical Images Deep Learning in Radiology Fuzzy Connectivity (FC) – Affinity functions • Absolute FC • Relative FC (and Iterative Relative FC) • Successful example applications of FC in medical imaging • Segmentation of Airway and Airway Walls using RFC based method Energy functional – Data and Smoothness terms • GraphCut – Min cut – Max Flow • ApplicationsinRadiologyImages
Template matching is a technique used to classify objects by comparing portions of images against templates. It involves moving a template image across a larger source image to find the best match based on pixel-by-pixel comparisons of brightness levels. For gray-level images, the difference in brightness levels at each pixel location is used rather than a simple yes/no match. Template matching is commonly used to identify simple objects like printed characters. Matlab examples demonstrate template matching on sample data sets and correlation maps show the strength of matches across the source images.
NeRF: Representing Scenes as Neural Radiance Fields for View Synthesis taeseon ryu
해당 논문은 3D Aware 모델입니다 StyleGAN 같은 경우에는 어떤 하나의 피처에 대해서 Editing 하고 싶을 때 입력에 해당하는 레이턴트 백터를 찾아서 레이턴트 백터를 수정함으로써 입에 해당하는 피쳐를 바꿀 수 있었는데 이런 컨셉을 그대로 착안해서
GAN 스페이스 논문에서는 인풋이 들어왔을 때 어떤 공간적인 정보까지도 에디팅하려고 시도했습니다 결과를 봤을 때 로테이션 정보가 어느 정도 잘 학습된 것 같지만 같은 사람이 아닌 것 같이 인식되기도 합니다 이러한 문제를 이제 disentangle 되지 않았다라고 하는 게 원하는 피처만 변화시켜야 되는 것과 달리 다른 피처까지도 모두 학습 모두 변했다는 것인데 이를 좀 더 효율적으로 3D를 더 잘 이해시키기 위해서 탄생한 논문입니다.
This document presents a methodology for motion blur image restoration using an alternating direction balanced regularization filter. It begins with an introduction discussing image restoration and types of image degradation like blur and noise. It then discusses a literature review of existing techniques for motion blur parameter estimation and image restoration. The proposed methodology is described as estimating the motion blur angle and length using Gabor filters and radial basis functions, then restoring the image using an alternating direction balanced regularization filter. Experimental results on various standard test images are provided, comparing the proposed method to existing techniques based on metrics like PSNR and MSE. The conclusions discuss that the proposed method provides improved restoration quality over existing methods.
Presentation for the Berlin Computer Vision Group, December 2020 on deep learning methods for image segmentation: Instance segmentation, semantic segmentation, and panoptic segmentation.
This document discusses camera models and image formation. It begins by describing the pinhole camera model and how a pinhole creates an image by blocking most light rays. A lens is then introduced to focus light rays onto film. Projection using the pinhole camera is modeled mathematically using homogeneous coordinates. Perspective projection is introduced, along with the camera projection matrix which models the camera's intrinsics and extrinsics. Distortion effects like radial distortion are also covered.
The document discusses sources of distortion in underwater images such as light scattering and color change. It proposes a method called Wavelength Compensation and Dehazing (WCID) to enhance underwater image visibility and color fidelity. WCID uses a hazy image formation model and dark channel prior to estimate depth maps and remove haze. It can also detect and remove effects of artificial light sources. The method is shown to outperform other dehazing techniques in experiments by achieving higher signal-to-noise ratios and more robust performance at different water depths.
The document describes a vehicle detection system using a fully convolutional regression network (FCRN). The FCRN is trained on patches from aerial images to predict a density map indicating vehicle locations. The proposed system is evaluated on two public datasets and achieves higher precision and recall than comparative shallow and deep learning methods for vehicle detection in aerial images. The system could help with applications like urban planning and traffic management.
An introduction to image processing in addition to explaining the concept of group operations.
Find me on:
AFCIT
http://www.afcit.xyz
YouTube
https://www.youtube.com/channel/UCuewOYbBXH5gwhfOrQOZOdw
Google Plus
https://plus.google.com/u/0/+AhmedGadIT
SlideShare
https://www.slideshare.net/AhmedGadFCIT
LinkedIn
https://www.linkedin.com/in/ahmedfgad/
ResearchGate
https://www.researchgate.net/profile/Ahmed_Gad13
Academia
https://www.academia.edu/
Google Scholar
https://scholar.google.com.eg/citations?user=r07tjocAAAAJ&hl=en
Mendelay
https://www.mendeley.com/profiles/ahmed-gad12/
ORCID
https://orcid.org/0000-0003-1978-8574
StackOverFlow
http://stackoverflow.com/users/5426539/ahmed-gad
Twitter
https://twitter.com/ahmedfgad
Facebook
https://www.facebook.com/ahmed.f.gadd
Pinterest
https://www.pinterest.com/ahmedfgad/
Los anaglifos fueron inventados en 1853 y permiten ver imágenes en 3D usando gafas especiales. En 1891 se realizaron las primeras proyecciones públicas con este método. En 1955 se inventó en España el sistema estereocrom que permitía anaglifos en color. En 1950 Ariznavarreta creó diapositivas anaglíficas en color y en 1954 publicó cromos anaglíficos de películas. Los anaglifos usan filtros de colores complementarios como rojo y cian para que cada ojo vea una imagen diferente y el
This document provides an overview of image enhancement techniques. It discusses the objectives of image enhancement, which is to process an image to make it more suitable for a specific application or task. The document focuses on spatial domain techniques for image enhancement, specifically point processing methods and histogram processing. It categorizes image enhancement methods into two broad categories: spatial domain methods, which directly manipulate pixel values; and frequency domain methods, which first convert the image into the frequency domain before performing enhancements.
The document discusses decision trees and random forests for machine learning. It begins with an overview and historical perspective on decision trees and random forests. It then describes how a decision tree is formed by splitting nodes based on features and assessing purity. Random forests grow multiple decision trees on bootstrapped data samples and aggregate their predictions. The document discusses applications in areas like computer vision, medical imaging, and engineering design. It covers computational complexity and variable importance analysis. Finally, it discusses current research challenges and opportunities in decision tree and random forest algorithms and architectures.
Automated attendance system based on facial recognitionDhanush Kasargod
A MATLAB based system to take attendance in a classroom automatically using a camera. This project was carried out as a final year project in our Electronics and Communications Engineering course. The entire MATLAB code I've uploaded it in mathworks.com. Also the entire report will be available at academia.edu page. Will be delighted to hear from you.
The document discusses various image enhancement techniques in Matlab, including filtering, predefined filters, image enhancement tools, image restoration, dilation/erosion functions, and dithering. Filtering can be used to modify images through operations like smoothing, sharpening, and edge enhancement. Predefined filters like 'gaussian' and 'laplacian' can be applied to images with functions like fspecial and imfilter. Additional tools for operations such as histogram equalization, noise addition, and filtering are also covered.
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.
The document discusses content-based image retrieval (CBIR). It provides a brief history of CBIR, noting it originated in 1992. It describes challenges of CBIR, including the semantic gap between low-level features extracted and high-level human concepts. It also outlines common CBIR techniques like color, shape, and texture analysis. Applications are described as image search and browsing. Limitations include not fully capturing human visual understanding.
This thesis presents research on using deep learning methods for feature extraction from satellite imagery to identify landslide pixels. The objectives are to classify land cover using machine learning algorithms like SVM and random forests in Google Earth Engine, design and evaluate a deep neural network for landslide identification, and compare performance of deep learning models in MATLAB. Results show that a neural network achieved over 98% accuracy at identifying landslide pixels. Future work proposes developing new indices for improved identification and an automatic landslide monitoring platform.
3D Reconstruction from Multiple uncalibrated 2D Images of an ObjectAnkur Tyagi
3D reconstruction is the process of capturing the shape and appearance of real objects. In this project we are using passive methods which only use sensors to measure the radiance reflected or emitted by the objects surface to infer its 3D structure.
This document summarizes a research paper that proposes a novel background removal algorithm using fuzzy c-means clustering. It begins by introducing background subtraction and some of the challenges. It then describes the proposed algorithm which uses edge detection to locate regions of interest before applying fuzzy c-means clustering to segment the foreground object. The algorithm achieves significant computation time reduction compared to other methods. Experimental results show the proposed method has higher true positive rates and accuracy compared to other algorithms, though precision and similarity are slightly lower.
This document summarizes an out-of-core rendering framework that can render massive 3D models that are larger than available memory. It uses ray casting and an acceleration structure to speed up ray intersection testing. The framework loads only relevant parts of the acceleration structure and model data into memory caches based on different replacement policies. It was tested on a 12 million triangle model and could render frames in around 21 seconds using an LRU cache policy.
Image fusion is a technique of
intertwining at least two pictures of same scene to
shape single melded picture which shows indispensable
data in the melded picture. Picture combination
system is utilized for expelling clamor from the
pictures. Commotion is an undesirable material which
crumbles the nature of a picture influencing the
lucidity of a picture. Clamor can be of different kinds,
for example, Gaussian commotion, motivation clamor,
uniform commotion and so forth. Pictures degenerate
some of the time amid securing or transmission or
because of blame memory areas in the equipment.
Picture combination should be possible at three
dimensions, for example, pixel level combination,
highlight level combination and choice dimension
combination. There are essentially two kinds of picture
combination methods which are spatial area
combination systems and transient space combination
procedures. (PCA) combination, Normal strategy, high
pass sifting are spatial area techniques and strategies
which incorporate change, for example, Discrete
Cosine Transform, Discrete wavelet change are
transient space combination strategies. There are
different techniques for picture combination which
have numerous favorable circumstances and
detriments. Numerous procedures experience the ill
effects of the issue of shading curios that comes in the
intertwined picture shaped. Also, the Cyclopean One
of the most astonishing properties of human stereo
vision is the combination of the left and right
perspectives of a scene into a solitary cyclopean one.
Under typical survey conditions, the world shows up as
observed from a virtual eye set halfway between the
left and right eye positions. The apparent picture of
the world is never recorded specifically by any tangible
exhibit, however developed by our neural equipment.
The term cyclopean alludes to a type of visual
upgrades that is characterized by binocular
dissimilarity alone. He suspected that stereo-psis may
find concealed articles, this may be helpful to discover
disguised items. The critical part of this examination
when utilizing arbitrary dab stereo-grams was that
uniqueness is adequate for stereo-psis, and where had
just demonstrated that binocular difference was vital
for stereo-psis.
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Three View Self Calibration and 3D Reconstruction
1. Camera Self Calibration and
Reconstruction from
Three Views
Peter Abeles
Date: May 2019
Copyright (C) 2019 Peter Abeles 1
2. Problem Statement
• 3-View Camera Self Calibration and 3D Reconstruction
• Focus on one possible solution. There are many others.
• Provides theory for “ThreeViewEstimateMetricScene” class in BoofCV
• Self Calibration
• Given a set of images of the same scene, estimate the camera’s intrinsic
parameters
• i.e. focal length, lens distortion, … etc
• Some basic assumptions are allowed
• Known pixel aspect ratio
• Known camera model, e.g. pinhole or fisheye
• No known calibration targets allowed
• e.g. no chessboard patterns
• Scene Reconstruction
• 3D location of observed features
• Camera pose, i.e. rotation and translation
• In most situations, to do self calibration, you also need to do scene
reconstruction
• Exceptions include; pure rotations and use of vanishing points
𝐾1, … , 𝐾 𝑛
(𝑅1, 𝑇1), … , (𝑅 𝑛, 𝑇𝑛)
𝑋1, … , 𝑋 𝑚
Intrinsic
Pose
Scene
+
Copyright (C) 2019 Peter Abeles 2
3. Required Background
• This is an advanced topic in 3D computer vision
• You need to already be familiar with the following
• Pinhole camera, epipolar geometry, projective geometry, fundamental
matrices, homographies, SVD, EVD, 3D Point Clouds, RANSAC
• Hartley and Zisserman, “Multiple View Geometry in Computer Vision”
2nd ed.
• Classic and most extensive text on this subject
• Not required but it is cited many times in this presentation
• Sometimes referred to as simply H&Z
Copyright (C) 2019 Peter Abeles 3
4. Why Just Three Views?
• 3-View contains all the interesting self
calibration math
• N-View is all about managing very large and
complex data structures
• N-View’s math is more forgiving and “less
interesting”
• 2-View is much more difficult than 3-View
• With 3-Views, geometry alone can eliminate
many of the false associations
• Many well known self calibration approaches
require 3 or more views
• We will come back to 2-View again at the end
• 1-View requires very strong assumptions
but is possible in specific situations
2-View
3-View
N-ViewsCopyright (C) 2019 Peter Abeles 4
5. What input images are ideal?
• Plenty of scene texture
• Translational camera motion
• Can’t reconstruct from pure
rotation
• Large baseline between views
• Better triangulation
• Small baseline between views
• Better feature matching
• Avoid extreme lighting
conditions
Copyright (C) 2019 Peter Abeles 5
6. 3-View Algorithm Overview (Part 1)
Feature Detection Associate 3-View Robust fit Trifocal
Tensor
Use best possible feature
detector, e.g. SIFT or
SURF. There’s also
promising research in
deep learning features.
Nearest-neighbor association.
Accepted only if 1→2→3→1.
RANSAC with a linear fit
for trifocal tensor and
reprojection error via
triangulation with non-
linear refinement.
Copyright (C) 2019 Peter Abeles 6
7. 3-View Algorithm Overview (Part 2)
𝑃2 =
𝑎11 𝑎12 𝑎13 𝑎14
𝑎21 𝑎22 𝑎23 𝑎24
𝑎31 𝑎32 𝑎33 𝑎34
𝑃1 =
1 0 0 0
0 1 0 0
0 0 1 0
𝑃3 =
𝑏11 𝑏12 𝑏13 𝑏14
𝑏21 𝑏22 𝑏23 𝑏24
𝑏31 𝑏32 𝑏33 𝑏34
Camera Matrices from
Trifocal Tensor
Absolute Dual Quadratic Metric Rectification of
Camera Matrices
Use Absolute Dual
Quadratic to compute a
rectifying homography H
Notoriously unstable to
estimate.
Arbitrary projective frame.
Compatible across all
views.
𝑄∞
∗
𝑤∗
= 𝑃𝑖 𝑄∞
∗
𝑃𝑖
𝑇
𝑤∗
= 𝐾𝐾 𝑇
𝑄∞
∗
= 𝐻 𝐼𝐻 𝑇
𝑃𝑖
𝑀
= 𝑃𝑖 𝐻
𝐾 is the 3x3 intrinsic matrix
𝑤∗
is the dual image of the
absolute conic
𝐻 is the rectifying homography
𝑃𝑖
𝑀
is the metric camera matrix
Copyright (C) 2019 Peter Abeles 7
8. 3-View Algorithm Overview (Part 3)
Construct Initial Estimate
of Scene
Bundle Adjustment Bundle Adjustment Again
Adjust initial camera
orientations and run SBA
multiple times.
Optimize all parameters at
once using an efficient sparse
bundle adjustment.
Triangulate 3D points
from previously estimated
camera locations.
𝑥 = 𝑃𝑖
𝑀
𝑋
𝑃𝑖
𝑀
= 𝐾𝑖 𝑅𝑖 𝑇𝑖
[1] Figures have been “borrowed” from the SBA Library documentation. SBA Library was not used in this project.
Copyright (C) 2019 Peter Abeles 8
9. Stereo Processing
Rectify Stereo Pair Dense Stereo Disparity 3D Point Cloud
Distort images so that epipolar
lines are at infinity..
Compute disparity of every pixel in
the image. Disparity is difference
between left and right images.
Going from disparity to a
3D point cloud is simple.
Copyright (C) 2019 Peter Abeles 9
10. 3D Point Cloud
• 3-View structure with 3D cloud from 2-
Views
• Created using the algorithm being
explained in this presentation
• Source code, images, and a pre-built
binaries available
• See end of presentation for links
• Notice how some of the images don’t
quite look right?
• e.g. stretched oddly
• Why don’t they look right?
• Converged to a local minima and got
focal length wrong
• Insufficient camera geometry
• e.g. baseline too small,
Copyright (C) 2019 Peter Abeles 10
11. Feature Detection
• Feature detectors find salient
features inside an image:
• 2D pixel coordinate
• N-tuple descriptor
• Rotation and scale invariant feature
detector and descriptor
recommended.
• E.g. SIFT [1]
• High quality implementations required
• 10% drop in stability significantly
increases instability
• BoofCV’s SURF [2] was used here [3]
Hessian Determinant Intensity
Selected SURF Features[1] Lowe, David G. "Object recognition from local scale-invariant features." ICCV. Vol. 99. No. 2. 1999.
[2] Bay, Herbert, Tinne Tuytelaars, and Luc Van Gool. "Surf: Speeded up robust features” ECCV. 2006.
[3] Abeles, P. “Speeding up SURF”. ISVC 2013
Copyright (C) 2019 Peter Abeles 11
12. 2-View Feature Association
Copyright (C) 2019 Peter Abeles 12
Features are described by a location
(x,y) and an N-Tuple
𝐹𝑖 = [𝑥1, … , 𝑥 𝑁]
Each feature in image A is associated
with a feature in image B by
minimizing the error
arg min
𝑗
𝐹𝑖
𝐴
− 𝐹𝑗
𝐵
A match is only accepted if the two
features are mutually each others
best choice
13. 3-View Association
Copyright (C) 2019 Peter Abeles 13
• Two view association is
performed for each image
pair
• Pairs: 1-2, 2-3, 3-1
• A feature is only accepted if it
is tracked successfully around
all 3 views back to itself
14. Metric vs Projective Camera
Metric
• Is a projective camera with
additional constraints
• A projective camera can be
“elevated” to metric by rectifying
homography H
• Reconstruction in Euclidean space
• Defined uniquely up to scale
Projective
• Any 3x4 matrix of rank 3
• Reconstruction will be in projective
space
• Very odd appearance
• Points easily move in and out of
infinity
• Uniquely defined up to a
homography
𝑃 𝑀 = 𝐾[𝑅|𝑇]
𝑃 𝑀 = 𝑃𝐻
K is 3x3 upper triangle intrinsic matrix
R is 3x3 rotation matrix
T is 3x1 translation vector
T is 3x1 translation vector
H is 4x4 projective to metric homography in 3-space
Copyright (C) 2019 Peter Abeles 14
15. Trifocal Tensor: Introduction
• Used to remove false associations and get
compatible projective cameras
• Trifocal tensor plays an analogous role in
three views that the fundamental matrix
does in two views [1]
• It is defined entirely by camera pose and
intrinsic parameters
• Given a trifocal tensor you can:
• Transfer: Give a view of a point or line in two
of the views estimate it’s location in third
• Extract Fundamental matrices 𝐹21, 𝐹31, 𝐹32
• Extract compatible projective camera
matrices 𝑃1, 𝑃2, 𝑃3
[1] Hartley and Zisserman, “Multiple View Geometry in Computer Vision”
[2] Figure by Marc Pollefeys
Relationship between a point and three
views. [2]
Copyright (C) 2019 Peter Abeles 15
16. Trifocal Tensor: Math Background
{𝑇1, 𝑇2, 𝑇3} 𝑇𝑖 ∈ ℝ3×3
In matrix notation a trifocal tensor is
described by a set of three 3x3 matrices
Relationship to Fundamental Matrices
𝐹21 = 𝑒′
x [𝑇1, 𝑇2, 𝑇3]𝑒′′
𝐹31 = 𝑒′′
x [𝑇3
𝑇
, 𝑇3
𝑇
, 𝑇3
𝑇
]𝑒′
𝑃1 = [I|0]
𝑃2 = [[𝑇1, 𝑇2, 𝑇3]𝑒′′
|𝑒′
]
𝑃3 = [(𝑒′′
𝑒′′𝑇
− I)[𝑇3
𝑇
, 𝑇3
𝑇
, 𝑇3
𝑇
]𝑒′
|𝑒′′
]
Relationship to Camera Matrices
𝐴 x is the 3x3 skew symmetric matrix of vector A 𝑒′
and 𝑒′′
are the epipoles in second and third image
Given three point correspondences
the following is true
An epipole is the point of intersection on the image plane between the principle point of two cameras.
𝑥′
x
𝑖
𝑥 𝑖 𝑇𝑖 𝑥′′
x = 03𝑥3
Copyright (C) 2019 Peter Abeles 16
17. Trifocal Tensor: Reprojection Error
• Reprojection error is needed for
RANSAC
• Attempted a few different
methods
• Point Transfer
• Triangulation
• Triangulation with Refinement
• Triangulation with Refinement
worked the best
1. Extract Camera matrices from Trifocal Tensor
2. Triangulate 3D point X in projective space
3. Refine 3D point by minimizing reprojection error
4. Select inliers using squared reprojection error
𝑃2 = [[𝑇1, 𝑇2, 𝑇3]𝑒′′
|𝑒′
]
𝑃3 = [(𝑒′′
𝑒′′𝑇
− I)[𝑇3
𝑇
, 𝑇3
𝑇
, 𝑇3
𝑇
]𝑒′
|𝑒′′
]
See page 312 for DLT in H&Z
𝑥𝑖 − 𝑋𝑃𝑖
2
min
𝑋
𝑥𝑖 − 𝑋𝑃𝑖
2
Copyright (C) 2019 Peter Abeles 17
𝑃𝑖 projective camera matrix 3x4
𝑥𝑖 pixel observation of feature X
18. Fundamental Matrices Instead of Trifocal?
• Can’t you just compute 𝐹21, 𝐹31, 𝐹32 instead of a trifocal tensor?
• Yes and probably the more popular approach
• Many if not most 3D vision libraries don’t even have a trifocal tensor!
• Disadvantages of Fundamental Matrix approach
• Applying epipolar constraint three times is less effective than applying a
trifocal constraint once
• Projective Camera matrices found by decomposing 𝐹21 and 𝐹31will not be
compatible
• Section 15.4 in Hartley and Zisserman
• Page 301 in Y. Ma, S. Soatto, J. Kosecka, and S. S. Sastry, "An Invitation to 3-D Vision"
Copyright (C) 2019 Peter Abeles 18
19. Fundamental Matrices Instead of Trifocal?
Two objects in front of a Camera
View 1 View 2 View 3
Epipolar Line
Apparent Location of Objects
• They all lie along the same epipolar line
• Pass epipolar tests, but would fail a trifocal
When you decompose a Fundamental matrix into two
projective matrices they have the following relationship
with a metric camera matrix
𝑃1
𝑀
= I 0 𝐻21 𝑃2
𝑀
= 𝑃2 𝐻21
𝑃1
𝑀
= I 0 𝐻31 𝑃3
𝑀
= 𝑃2 𝐻31
𝑃2
𝑀
= I 0 𝐻32 𝑃3
𝑀
= 𝑃3 𝐻31
𝐹21
𝐹31
𝐹32
• Notice how the rectifying homography 𝐻𝑖𝑗 is
different for each decomposition?
• It is possible to find a transform for each
decomposition which will take them to a single
compatible frame
• This is similar to scale ambiguity
Copyright (C) 2019 Peter Abeles 19
20. Absolute Dual Quadratic (Part 1)
𝑃𝑖
𝑀
= 𝑃𝑖 𝐻𝑃𝑖
𝑀
= 𝐾𝑖[𝑅𝑖|𝑇𝑖]
𝑃1 =[I|0] 𝑃1
𝑀
= 𝐾1[𝐼|0]
𝐻 =
𝐾1 0
𝑣 𝑇
1
𝜋∞ = (𝑝 𝑇, 1) 𝑇
𝑃𝑖 = [𝐴𝑖|𝑎𝑖]
ADQ is used to upgrade a projective camera into a metric camera
A metric camera matrix 𝑃𝑖
𝑀
is related to a projective camera matrix 𝑃𝑖 by a homography H
We can select the origin/initial projective camera matrix arbitrarily, to make the math
easier we define it as follows:
From this it follows that
(1)
(2)
(3)
𝜋∞ = 𝐻−𝑇
0
0
0
1
𝑝 = − 𝐾1
−𝑇
𝑣
From which the plane at infinity is derivedThen we define
(4)
𝜋∞ is the plane at infinity
𝐻 is projective to metric homography. 4x4
𝑣 is an arbitrary 3x1 vector Copyright (C) 2019 Peter Abeles 20
𝑃𝑖
𝑀
is a metric camera matrix. 3x4
𝑃𝑖 is a projective camera matrix.
3x4
21. Absolute Dual Quadratic (Part 2)
Using equations (1,3,4) in the previous slide you can derive
𝐾𝑖 𝐾𝑖
𝑇
∈ ℝ3×3
= 𝐴𝑖 − 𝑎𝑖 𝑝 𝑇
𝐾1 𝐾1
𝑇
𝐴𝑖 − 𝑎𝑖 𝑝 𝑇 𝑇
𝑤𝑖
∗
= 𝐾𝑖 𝐾𝑖
𝑇
= 𝑃𝑖 𝑄∞
∗
𝑃𝑖
𝑇
= 𝐴𝑖 − 𝑎𝑖 𝑝 𝑇
𝑤1
∗
𝐴𝑖 − 𝑎𝑖 𝑝 𝑇 𝑇
𝑄∞
∗ ∈ ℝ4×4 = 𝐻 𝐼𝐻 𝑇 =
𝑤1
∗
−𝑤1
∗
𝑝
−𝑝 𝑇
𝑤1
∗
𝑝 𝑇
𝑤1
∗
𝑝
From which we then define the dual image of the absolute quadratic 𝑤𝑖
∗
The final step is to use the known structure of 𝑤1
∗
and the already found values of 𝑃𝑖
to compute 𝑄∞
∗
From this we define the Absolute Dual Quadratic 𝑄∞
∗
, which is a 4x4 matrix
Notice how 𝑤𝑖
∗
for view 𝑖 only depends on the unknowns p and 𝑤1
∗
?
Copyright (C) 2019 Peter Abeles 21
𝐾𝑖 is a 3x3 upper
triangular intrinsic
camera matrix
𝐴𝑖 is 3x3 sub-matrix in 𝑃𝑖
𝑝 is from 𝜋∞ = (𝑝 𝑇
, 1) 𝑇
𝐼 is diag(1,1,1,0)
𝑃𝑖 is a projective camera
matrix. 3x4
𝐻 see past 20 slides . You know complaining that
every variable isn’t defined in very slide is really
silly?
22. Solving for Absolute Dual Quadratic (Part 1)
𝑤∗
= 𝐾𝑖 𝐾𝑖
𝑇
=
𝑓𝑥
2 + 𝑐 𝑥
2 𝑐 𝑥 𝑐 𝑦 𝑐 𝑥
𝑐 𝑥 𝑐 𝑦 𝑓𝑦
2 + 𝑐 𝑦
2 𝑐 𝑦
𝑐 𝑥 𝑐 𝑦 1
K=
𝑓𝑥 0 𝑐 𝑥
0 𝑓𝑦 𝑐 𝑦
0 0 1
Intrinsic Camera
Matrix with zero
skew
Known structure
of 𝑤∗
from K
• Now assume the principle point (𝑐 𝑥, 𝑐 𝑦) is (0,0)
• This can be accomplished by assuming the image center
is (𝑐 𝑥, 𝑐 𝑦) and subtracting that from all pixels.
• Calibration is much less sensitive to errors in the
principle point
𝑤∗
=
𝑓𝑥
2 0 0
0 𝑓𝑦
2
0
0 0 1
These known zeros will now be
used to solve for 𝑄∞
∗
Copyright (C) 2019 Peter Abeles 22
(𝑓𝑥, 𝑓𝑦) is the camera’s focal length
Copyright (C) 2019 Peter Abeles 22
23. Solving for Absolute Dual Quadratic (Part 2)
• You now have 𝑃𝑖 for 3 views and you know that 𝐾𝑖 has zero skew and zero principle points.
• Using the known zeros in 𝑤𝑖
∗
, that gives you 3 equations for each view.
• 𝑄∞
∗
is a symmetric 4x4 and can be parameterized by 10 unknowns
• With a bit of algebra it’s possible to reformat (2) into a linear system and solve for the null
space using SVD
• With 3 constraints per view this would require 4 views to solve for.
• If you add the constraint 𝑓𝑥 = 𝑓𝑦 then only 3 views are needed
• The equations are quite ugly and I wrote Sage Math code for generating them
• See (unreleased) BoofCV technical report [1]
𝑤𝑖
∗
= 𝑃𝑖 𝑄∞
∗ 𝑃𝑖
𝑇
𝑃𝑖 𝑄∞
∗ 𝑃𝑖
𝑇
13
= 0 𝑃𝑖 𝑄∞
∗ 𝑃𝑖
𝑇
23
= 0 𝑃𝑖 𝑄∞
∗
𝑃𝑖
𝑇
12
= 0
[1] Promise that I’ll release this “soon”
Copyright (C) 2019 Peter Abeles 23
(1)
(2)
24. Projective to Metric
Recall that the absolute dual quadratic 𝑄∞
∗ can be
decomposed into
𝑄∞
∗
= 𝐻 𝐼𝐻 𝑇
Where 𝐻 a 4x4 projective to metric homography
and 𝐼 is diag(1,1,1,0).
H can thus be found using Eigenvalue
Decomposition [1] or by directly solving for 𝑤1
∗
which is the same as solving for 𝐾1. In this
example we used the later.
A = chol(inv(Q(1:3,1:3)))’
K = inv(A)
K = K./K(3,3)
p = -inv(K*K’)*Q(1:3,4)
H = [K [0;0;0];-p’*K 1]
BoofCV’s implementation contains additional
manipulations to scale variables and handle
degenerate situations.
Untested Matlab code for direct solution
[1] Page 463 in Hartley and Zisserman, “Multiple View Geometry in Computer Vision”
Copyright (C) 2019 Peter Abeles 24
25. Initial Reconstruction
• We now have for each view
• 𝐾𝑖 intrinsic parameters
• 𝑅𝑖 and 𝑇𝑖 rotation and translation
• 𝑅1and 𝑇1are identity and (0,0,0)
• What we need are the 3D
locations of each feature
• Find using triangulation
3-View Metric Triangulation
Initial Estimate using DLT
Page 312 in H&Z
Non-Linear Refinement
of Residual Error
Residual = 𝑥 − 𝐾 𝑅 𝑇 𝑋
Copyright (C) 2019 Peter Abeles 25
26. Refine Reconstruction
• Initial reconstruction is very crude
and not good enough to compute a
dense 3D cloud from
• Improve initial reconstruction using
sparse bundle adjustment [1]
• Sensitive to initial parameters
• Run multiple times
• Orientation physically impossible? Try
flipping initial orientation
• Remove outlier 3D features and run
again
• Select solution with minimal residual
error and is physically possible
Steps fx change |step| f-test g-test tr-ratio lambda
0 8.815E+04 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.00 1.00E-03
1 2.157E+02 -8.794E+04 3.118E+00 9.976E-01 2.832E+00 1.000 3.33E-04
…
15 3.253E+01 -4.782E-05 8.401E-01 1.470E-06 8.591E-03 0.745 2.47E-07
16 3.253E+01 -3.092E-05 8.615E-01 9.507E-07 7.473E-03 0.595 2.45E-07
Converged f-test
Before After
𝑓1 405.4 340.9
𝑓2 406.0 340.4
𝑓3 405.5 340.4
Verbose output from BoofCV’s implementation
Quality of solution is strongly dependent on initial
focal length estimates
fx is sum of residual error. ~1000x improvement
Copyright (C) 2019 Peter Abeles 26
[1] Triggs, Bill, et al. "Bundle Adjustment— A Modern Synthesis." 1999.
27. Stereo Processing
Rectify Stereo Pair Dense Stereo Disparity 3D Point Cloud
Distort images so that epipolar
lines are at infinity. [1]
Compute disparity of every pixel in
the image. Disparity is difference
between left and right images. [2]
Going from disparity to a
3D point cloud is simple.
[1] A. Fusiello, E. Trucco, and A. Verri, "A Compact Algorithm for Rectification of Stereo Pairs“ Machine Vision and Applications, 2000
[2] Heiko Hirschmuller, Peter R. Innocent, and Jon Garibaldi. "Real-Time Correlation-Based Stereo Vision with Reduced Border Errors." Int. J. Comput. Vision 47, 1-3 2002
Copyright (C) 2019 Peter Abeles 27
• Most implementations use Multiview Stereo for dense reconstruction
• Here dense two view stereo was used due to availability
28. How Practical is this?
• Reconstruction from three views has no known truly stable numerical
solution
• The literature is a bit of a graveyard
• Paper Y presents a new solution and mentions they were unable to replicate results in X
• Paper Z presents a new solution and mentions they were unable to replicate results in Y
• Having identical image features but changing their order will produce different
solutions
• Discovered when a concurrent feature detector was added
• Most reconstruction tools require many more than 3 views and often
“cheat” by using known focal length from EXIF data
• The algorithm presented here converges to a reasonable solution about
70%, if given good input images
Copyright (C) 2019 Peter Abeles 28
29. Two View Reconstruction
• It’s possible to follow much the same pipe line
with two views and create a 3D reconstruction!
• False positive associations are much more
numerous
• Epipolar constraint is insufficient
• Difficult to obtain an initial estimate for K
• Guess and check often works
• Even less stable than 3-View Case
• Converges about 35% of the time with an ideal scene
Copyright (C) 2019 Peter Abeles 29
Highly distorted
stereo rectified
image from 2-View
Successful stereo
rectification
30. Topics Not Discussed
• Homogenous coordinates vs Regular 2D and 3D
• When should you use what type?
• How to parameterize rotation matrices
• Rodrigues coordinates were used
• Proper normalization of input data
• In general keep everything having a magnitude of about 1
• Exception handling
• What do you do if a matrix is degenerate?
• Recent research
• New geometric algorithms
• Deep learning based approaches
Copyright (C) 2019 Peter Abeles 30
31. Papers and Software
Books / Papers
• Multiple View Geometry
• An Invitation to 3D Vision
• Build Rome in a Day
• Bundle adjustment—A Modern
synthesis
• Direct Methods for Sparse Linear
Systems
Libraries
• BoofCV (Used here)
• Ceres Solver
• COLMAP
• Theia SFM
• Patch-based Multi-view Stereo
• Alice Vision
• SBA
A lot of research has gone into this topic. Here are some places to start learning more.
Apologies to all the papers/libraries that are missed!
Copyright (C) 2019 Peter Abeles 31
32. Source Code and Applications
Presented results were generated using
examples and demonstration code
found in BoofCV (Github)
• Source code for three view
https://boofcv.org/index.php?title=Example_Three_View_Stereo_Uncalibrated
• Source code for two view
https://boofcv.org/index.php?title=Example_Stereo_Uncalibrated
• More robust and complex three
view solution
https://github.com/lessthanoptimal/BoofCV/blob/master/main/boofcv-
sfm/src/main/java/boofcv/alg/sfm/structure/ThreeViewEstimateMetricScene.java
Pre-built application are available
• Demonstration application (link)
• SFM 3D -> DemoThreeViewStereoApp
• Can dynamically adjust some settings
• Open images on your computer
• Pre-built example code can be run
using the same application
Copyright (C) 2019 Peter Abeles 32
Editor's Notes
A common theme in computer vision in recent years is that more data is better than more advanced algorithms.
This lesson was learned a while ago in Multiview reconstruction. The focus in that field has been in how to get a crude initial estimate of the scene, then use a ton of data to refine and recover from initial mistakes.
In contrast, this presentation is focused on how to get the best initial estimate given only a little bit of data.
For the next several slides the math is going to get a bit more intense. Instead of going over each derivation in detail I will focus on what they enable to find.
SBA is a specialized form of least-square optimization. Typically implemented using Schur decomposition and a trust-region based algorithm like Levenberg-Marqardt. Different techniques are used depending on the size of your dataset.
For an algorithm to be of practical use it needs to work quite often on real data. Often times algorithms presented in books and papers are not practical and the results cherry picked. There is a proud tradition in computer vision of selecting the one time an algorithm worked from the 20 times it failed. The goal is to just show that it can work at all right?