This document provides an overview of morphological image processing techniques. It begins with introductions to morphology, structuring elements, erosion, dilation, opening, closing, and hit-or-miss transformations. Examples are given for each. The document then describes basic morphological algorithms for boundary extraction, hole filling, connected component extraction, convex hulls, thinning, thickening, and skeletonization. Pruning, morphological reconstruction, and geodesic dilation are also summarized. Overall, the document covers fundamental concepts and operations in morphological image processing.
This document summarizes key concepts in morphological image processing including dilation, erosion, opening, closing, and hit-or-miss transformations. Morphological operations manipulate image shapes and structures using structuring elements based on set theory operations. Dilation adds pixels to the boundaries of objects in an image, while erosion removes pixels on object boundaries. Opening can remove noise and smooth object contours, while closing can fill in small holes and fill gaps in object shapes. Hit-or-miss transformations are used to detect specific patterns of on and off pixels. These operations form the basis for morphological algorithms like boundary extraction.
This document provides an overview of mathematical morphology and its applications to image processing. Some key points:
- Mathematical morphology uses concepts from set theory and uses structuring elements to probe and extract image properties. It provides tools for tasks like noise removal, thinning, and shape analysis.
- Basic operations include erosion, dilation, opening, and closing. Erosion shrinks objects while dilation expands them. Opening and closing combine these to smooth contours or fill gaps.
- Hit-or-miss transforms allow detecting specific shapes. Skeletonization reduces objects to 1-pixel wide representations.
- Morphological operations can be applied to binary or grayscale images. Structuring elements are used to specify the neighborhood of pixels
Morphological image processing uses mathematical morphology tools to extract image components and describe shapes. Some key tools include binary erosion and dilation, which thin and thicken objects. Erosion shrinks objects while dilation grows them. Opening and closing are combinations of erosion and dilation that smooth contours or fill gaps. The hit-or-miss transform detects shapes by requiring matches of foreground and background pixels. Other algorithms include boundary extraction, hole filling, and thinning to find skeletons, which are medial axes of object shapes.
The document discusses various morphological image processing techniques including binary morphology, grayscale morphology, dilation, erosion, opening, closing, boundary extraction, region filling, connected components, hit-or-miss, thinning, thickening, and skeletonization. Morphological operations can be used for tasks like edge detection, noise removal, image enhancement, and image segmentation. The key morphological operations of dilation and erosion expand and shrink binary images using a structuring element, while opening and closing combine these operations to remove noise or fill holes.
Image Enhancement: Introduction to Spatial Filters, Low Pass Filter and High Pass Filters. Here Discussed Image Smoothing and Image Sharping, Gaussian Filters
This document discusses morphological operations in image processing. It describes how morphological operations like erosion, dilation, opening, and closing can be used to extract shapes and boundaries from binary and grayscale images. Erosion shrinks foreground regions while dilation expands them. Opening performs erosion followed by dilation to remove noise, and closing does the opposite to join broken parts. The hit-and-miss transform is also introduced to detect patterns in binary images using a structuring element containing foreground and background pixels. Examples are provided to illustrate each morphological operation.
The document discusses mathematical morphology and its applications in image processing. It begins with introductions to morphological image processing and concepts from set theory. It then covers basic morphological operations like dilation, erosion, opening and closing for binary images. It also discusses their extensions to grayscale images. Examples are provided to illustrate concepts like dilation, erosion, hit-or-miss transform, boundary extraction, region filling and skeletonization. The document provides a comprehensive overview of mathematical morphology and its role in tasks like preprocessing, segmentation and feature extraction in digital image analysis.
This document discusses different approaches to implementing scope rules in programming languages. It begins by defining lexical/static scope and dynamic scope. It then discusses how block structure and nested procedures can be implemented using stacks and access links. Specifically, it describes how storage is allocated for local and non-local variables under lexical and dynamic scope models. The key implementation techniques discussed are stacks, access links, displays, deep access, and shallow access.
This document summarizes key concepts in morphological image processing including dilation, erosion, opening, closing, and hit-or-miss transformations. Morphological operations manipulate image shapes and structures using structuring elements based on set theory operations. Dilation adds pixels to the boundaries of objects in an image, while erosion removes pixels on object boundaries. Opening can remove noise and smooth object contours, while closing can fill in small holes and fill gaps in object shapes. Hit-or-miss transformations are used to detect specific patterns of on and off pixels. These operations form the basis for morphological algorithms like boundary extraction.
This document provides an overview of mathematical morphology and its applications to image processing. Some key points:
- Mathematical morphology uses concepts from set theory and uses structuring elements to probe and extract image properties. It provides tools for tasks like noise removal, thinning, and shape analysis.
- Basic operations include erosion, dilation, opening, and closing. Erosion shrinks objects while dilation expands them. Opening and closing combine these to smooth contours or fill gaps.
- Hit-or-miss transforms allow detecting specific shapes. Skeletonization reduces objects to 1-pixel wide representations.
- Morphological operations can be applied to binary or grayscale images. Structuring elements are used to specify the neighborhood of pixels
Morphological image processing uses mathematical morphology tools to extract image components and describe shapes. Some key tools include binary erosion and dilation, which thin and thicken objects. Erosion shrinks objects while dilation grows them. Opening and closing are combinations of erosion and dilation that smooth contours or fill gaps. The hit-or-miss transform detects shapes by requiring matches of foreground and background pixels. Other algorithms include boundary extraction, hole filling, and thinning to find skeletons, which are medial axes of object shapes.
The document discusses various morphological image processing techniques including binary morphology, grayscale morphology, dilation, erosion, opening, closing, boundary extraction, region filling, connected components, hit-or-miss, thinning, thickening, and skeletonization. Morphological operations can be used for tasks like edge detection, noise removal, image enhancement, and image segmentation. The key morphological operations of dilation and erosion expand and shrink binary images using a structuring element, while opening and closing combine these operations to remove noise or fill holes.
Image Enhancement: Introduction to Spatial Filters, Low Pass Filter and High Pass Filters. Here Discussed Image Smoothing and Image Sharping, Gaussian Filters
This document discusses morphological operations in image processing. It describes how morphological operations like erosion, dilation, opening, and closing can be used to extract shapes and boundaries from binary and grayscale images. Erosion shrinks foreground regions while dilation expands them. Opening performs erosion followed by dilation to remove noise, and closing does the opposite to join broken parts. The hit-and-miss transform is also introduced to detect patterns in binary images using a structuring element containing foreground and background pixels. Examples are provided to illustrate each morphological operation.
The document discusses mathematical morphology and its applications in image processing. It begins with introductions to morphological image processing and concepts from set theory. It then covers basic morphological operations like dilation, erosion, opening and closing for binary images. It also discusses their extensions to grayscale images. Examples are provided to illustrate concepts like dilation, erosion, hit-or-miss transform, boundary extraction, region filling and skeletonization. The document provides a comprehensive overview of mathematical morphology and its role in tasks like preprocessing, segmentation and feature extraction in digital image analysis.
This document discusses different approaches to implementing scope rules in programming languages. It begins by defining lexical/static scope and dynamic scope. It then discusses how block structure and nested procedures can be implemented using stacks and access links. Specifically, it describes how storage is allocated for local and non-local variables under lexical and dynamic scope models. The key implementation techniques discussed are stacks, access links, displays, deep access, and shallow access.
This document discusses techniques for image compression including bit-plane coding, bit-plane decomposition, constant area coding, and run-length coding. It explains that bit-plane decomposition represents a grayscale image as a collection of binary images based on its representation as a binary polynomial. Run-length coding compresses each row of a binary image by coding contiguous runs of 0s or 1s with their length, separately for black and white runs. Constant area coding classifies blocks of pixels as all white, all black, or mixed and codes them with special codewords.
This document provides an overview of digital image processing techniques for image restoration. It defines image restoration as improving a degraded image using prior knowledge of the degradation process. The goal is to recover the original image by applying an inverse process to the degradation function. Common degradation sources are discussed, along with noise models like Gaussian, salt and pepper, and periodic noise. Spatial and frequency domain filtering techniques are presented for restoration, such as mean, median and inverse filters. The maximum mean square error or Wiener filter is also introduced as a way to minimize restoration error.
its very useful for students.
Sharpening process in spatial domain
Direct Manipulation of image Pixels.
The objective of Sharpening is to highlight transitions in intensity
The image blurring is accomplished by pixel averaging in a neighborhood.
Since averaging is analogous to integration.
Prepared by
M. Sahaya Pretha
Department of Computer Science and Engineering,
MS University, Tirunelveli Dist, Tamilnadu.
This document summarizes techniques for least mean square filtering and geometric transformations. It discusses minimum mean square error (Wiener) filtering, constrained least squares filtering, and geometric mean filtering for noise removal. It also covers spatial transformations, nearest neighbor gray level interpolation, and bilinear interpolation for geometric correction of distorted images. Examples are provided to demonstrate geometric distortion, nearest neighbor interpolation, and bilinear transformation.
This document provides an overview of mathematical morphology and its applications in image processing. Some key points:
- Mathematical morphology uses concepts from set theory and uses structuring elements to probe and modify binary and grayscale images.
- Basic morphological operations include erosion, dilation, opening, closing, hit-or-miss transformation, thinning, thickening, and skeletonization.
- Erosion shrinks objects and removes small details while dilation expands objects and fills small holes. Opening and closing combine these to smooth contours or fuse breaks.
- Morphological operations have many applications including boundary extraction, region filling, component labeling, convex hulls, pruning, and more. Grayscale images extend these concepts using minimum/maximum
Lecture 16 KL Transform in Image ProcessingVARUN KUMAR
The KL transform is a data-driven transformation where the kernel is derived from the statistics of the data, unlike transforms like DFT where the kernel is fixed. (1) It represents data as a vector based on the mean and covariance matrix of the population. (2) The transformation matrix is chosen such that the transformed data is statistically uncorrelated and ordered by decreasing variance. (3) This transformation optimally compacts the energy but requires high computational complexity.
This document discusses morphological image processing using mathematical morphology. It begins with an introduction to morphology in biology and its application to image analysis using set theory. The key concepts of dilation, erosion, opening and closing are explained. Dilation expands object boundaries while erosion shrinks them. Opening performs erosion followed by dilation to smooth contours, and closing performs dilation followed by erosion to fill small holes. Structuring elements determine the shape and size of operations. Morphological operations are useful for tasks like boundary extraction, noise removal, and feature detection.
Image compression involves reducing the size of image files to reduce storage space and transmission time. There are three main types of redundancy in images: coding redundancy, spatial redundancy between neighboring pixels, and irrelevant information. Common compression methods remove these redundancies, such as Huffman coding, arithmetic coding, LZW coding, and run length coding. Popular image file formats include JPEG for photos, PNG for web images, and TIFF, GIF, and DICOM for other uses.
Digital images can be enhanced in various ways to improve quality. There are three main categories of enhancement techniques: spatial domain, frequency domain, and combination methods. Spatial domain methods operate directly on pixel values using point processing or neighborhood filtering. Key spatial techniques include contrast stretching, thresholding, and histogram equalization. Frequency domain methods modify an image's Fourier transform. Common transformations include logarithmic, power-law, and piecewise linear functions, which can increase contrast or highlight certain grayscale ranges. Proper enhancement improves an image's features for desired applications.
This document discusses digital image compression. It notes that compression is needed due to the huge amounts of digital data. The goals of compression are to reduce data size by removing redundant data and transforming the data prior to storage and transmission. Compression can be lossy or lossless. There are three main types of redundancy in digital images - coding, interpixel, and psychovisual - that compression aims to reduce. Channel encoding can also be used to add controlled redundancy to protect the source encoded data when transmitted over noisy channels. Common compression methods exploit these different types of redundancies.
This document discusses color image processing and provides information on various color models and color fundamentals. It describes full-color and pseudo-color processing, color fundamentals including the visible light spectrum, color perception by the human eye, and color properties. It also summarizes RGB, CMY/CMYK, and HSI color models, conversions between models, and methods for pseudo-color image processing including intensity slicing and intensity to color transformations.
This document discusses image restoration techniques for noise removal, including:
- Spatial domain filtering techniques like mean, median, and order statistics filters to remove random noise.
- Frequency domain filtering like band reject filters to remove periodic noise.
- Adaptive filtering techniques where the filter size changes depending on image characteristics within the filter region to better handle impulse noise.
This document provides an overview of deterministic finite automata (DFA) through examples and practice problems. It begins with defining the components of a DFA, including states, alphabet, transition function, start state, and accepting states. An example DFA is given to recognize strings ending in "00". Additional practice problems involve drawing minimal DFAs, determining the minimum number of states for a language, and completing partially drawn DFAs. The document aims to help students learn and practice working with DFA models.
This document discusses various frequency domain image filtering techniques. It outlines the basic steps for filtering in the frequency domain which includes centering the Fourier transform, computing the discrete Fourier transform, multiplying by a filter function, computing the inverse transform and canceling centering operations. Specific filters are then described including low pass, high pass, ideal filters and Butterworth filters. Examples of applying these filters to images are provided to demonstrate the effects. Homomorphic filtering is also introduced as a technique for illumination correction.
Intensity Transformation and Spatial filteringShajun Nisha
Dr. S. Shajun Nisha discusses intensity transformation and spatial filtering techniques in image processing. Intensity transformation functions modify pixel intensities based on a transformation function. Spatial filtering involves applying an operator over a neighborhood of pixels. Common intensity transformations include contrast stretching and logarithmic transforms. Histogram equalization is also described to improve contrast. Spatial filters include linear filters implemented using imfilter and non-linear filters like median filtering with ordfilt2 and medfilt2. Examples demonstrate applying these techniques to enhance images.
Fuzzy sets allow for gradual membership of elements in a set, rather than binary membership as in classical set theory. Membership is described on a scale of 0 to 1 using a membership function. Fuzzy sets generalize classical sets by treating classical sets as special cases where membership values are restricted to 0 or 1. Fuzzy set theory can model imprecise or uncertain information and is used in domains like bioinformatics. Examples of fuzzy sets include sets like "tall people" where membership in the set is a matter of degree.
Morphological image processing uses small image patterns called structuring elements to probe and modify binary images. Basic morphological operations include erosion, dilation, opening, closing, and hit-or-miss transformation. Erosion shrinks objects and removes small details, while dilation expands objects and fills small holes. Opening performs erosion followed by dilation to smooth contours and break thin connections. Closing performs dilation followed by erosion to smooth contours but fuse breaks and fill holes. Hit-or-miss is used to detect specific shapes. Morphological operations have applications in boundary extraction, hole filling, thinning, thickening, and feature detection.
This document discusses techniques for image compression including bit-plane coding, bit-plane decomposition, constant area coding, and run-length coding. It explains that bit-plane decomposition represents a grayscale image as a collection of binary images based on its representation as a binary polynomial. Run-length coding compresses each row of a binary image by coding contiguous runs of 0s or 1s with their length, separately for black and white runs. Constant area coding classifies blocks of pixels as all white, all black, or mixed and codes them with special codewords.
This document provides an overview of digital image processing techniques for image restoration. It defines image restoration as improving a degraded image using prior knowledge of the degradation process. The goal is to recover the original image by applying an inverse process to the degradation function. Common degradation sources are discussed, along with noise models like Gaussian, salt and pepper, and periodic noise. Spatial and frequency domain filtering techniques are presented for restoration, such as mean, median and inverse filters. The maximum mean square error or Wiener filter is also introduced as a way to minimize restoration error.
its very useful for students.
Sharpening process in spatial domain
Direct Manipulation of image Pixels.
The objective of Sharpening is to highlight transitions in intensity
The image blurring is accomplished by pixel averaging in a neighborhood.
Since averaging is analogous to integration.
Prepared by
M. Sahaya Pretha
Department of Computer Science and Engineering,
MS University, Tirunelveli Dist, Tamilnadu.
This document summarizes techniques for least mean square filtering and geometric transformations. It discusses minimum mean square error (Wiener) filtering, constrained least squares filtering, and geometric mean filtering for noise removal. It also covers spatial transformations, nearest neighbor gray level interpolation, and bilinear interpolation for geometric correction of distorted images. Examples are provided to demonstrate geometric distortion, nearest neighbor interpolation, and bilinear transformation.
This document provides an overview of mathematical morphology and its applications in image processing. Some key points:
- Mathematical morphology uses concepts from set theory and uses structuring elements to probe and modify binary and grayscale images.
- Basic morphological operations include erosion, dilation, opening, closing, hit-or-miss transformation, thinning, thickening, and skeletonization.
- Erosion shrinks objects and removes small details while dilation expands objects and fills small holes. Opening and closing combine these to smooth contours or fuse breaks.
- Morphological operations have many applications including boundary extraction, region filling, component labeling, convex hulls, pruning, and more. Grayscale images extend these concepts using minimum/maximum
Lecture 16 KL Transform in Image ProcessingVARUN KUMAR
The KL transform is a data-driven transformation where the kernel is derived from the statistics of the data, unlike transforms like DFT where the kernel is fixed. (1) It represents data as a vector based on the mean and covariance matrix of the population. (2) The transformation matrix is chosen such that the transformed data is statistically uncorrelated and ordered by decreasing variance. (3) This transformation optimally compacts the energy but requires high computational complexity.
This document discusses morphological image processing using mathematical morphology. It begins with an introduction to morphology in biology and its application to image analysis using set theory. The key concepts of dilation, erosion, opening and closing are explained. Dilation expands object boundaries while erosion shrinks them. Opening performs erosion followed by dilation to smooth contours, and closing performs dilation followed by erosion to fill small holes. Structuring elements determine the shape and size of operations. Morphological operations are useful for tasks like boundary extraction, noise removal, and feature detection.
Image compression involves reducing the size of image files to reduce storage space and transmission time. There are three main types of redundancy in images: coding redundancy, spatial redundancy between neighboring pixels, and irrelevant information. Common compression methods remove these redundancies, such as Huffman coding, arithmetic coding, LZW coding, and run length coding. Popular image file formats include JPEG for photos, PNG for web images, and TIFF, GIF, and DICOM for other uses.
Digital images can be enhanced in various ways to improve quality. There are three main categories of enhancement techniques: spatial domain, frequency domain, and combination methods. Spatial domain methods operate directly on pixel values using point processing or neighborhood filtering. Key spatial techniques include contrast stretching, thresholding, and histogram equalization. Frequency domain methods modify an image's Fourier transform. Common transformations include logarithmic, power-law, and piecewise linear functions, which can increase contrast or highlight certain grayscale ranges. Proper enhancement improves an image's features for desired applications.
This document discusses digital image compression. It notes that compression is needed due to the huge amounts of digital data. The goals of compression are to reduce data size by removing redundant data and transforming the data prior to storage and transmission. Compression can be lossy or lossless. There are three main types of redundancy in digital images - coding, interpixel, and psychovisual - that compression aims to reduce. Channel encoding can also be used to add controlled redundancy to protect the source encoded data when transmitted over noisy channels. Common compression methods exploit these different types of redundancies.
This document discusses color image processing and provides information on various color models and color fundamentals. It describes full-color and pseudo-color processing, color fundamentals including the visible light spectrum, color perception by the human eye, and color properties. It also summarizes RGB, CMY/CMYK, and HSI color models, conversions between models, and methods for pseudo-color image processing including intensity slicing and intensity to color transformations.
This document discusses image restoration techniques for noise removal, including:
- Spatial domain filtering techniques like mean, median, and order statistics filters to remove random noise.
- Frequency domain filtering like band reject filters to remove periodic noise.
- Adaptive filtering techniques where the filter size changes depending on image characteristics within the filter region to better handle impulse noise.
This document provides an overview of deterministic finite automata (DFA) through examples and practice problems. It begins with defining the components of a DFA, including states, alphabet, transition function, start state, and accepting states. An example DFA is given to recognize strings ending in "00". Additional practice problems involve drawing minimal DFAs, determining the minimum number of states for a language, and completing partially drawn DFAs. The document aims to help students learn and practice working with DFA models.
This document discusses various frequency domain image filtering techniques. It outlines the basic steps for filtering in the frequency domain which includes centering the Fourier transform, computing the discrete Fourier transform, multiplying by a filter function, computing the inverse transform and canceling centering operations. Specific filters are then described including low pass, high pass, ideal filters and Butterworth filters. Examples of applying these filters to images are provided to demonstrate the effects. Homomorphic filtering is also introduced as a technique for illumination correction.
Intensity Transformation and Spatial filteringShajun Nisha
Dr. S. Shajun Nisha discusses intensity transformation and spatial filtering techniques in image processing. Intensity transformation functions modify pixel intensities based on a transformation function. Spatial filtering involves applying an operator over a neighborhood of pixels. Common intensity transformations include contrast stretching and logarithmic transforms. Histogram equalization is also described to improve contrast. Spatial filters include linear filters implemented using imfilter and non-linear filters like median filtering with ordfilt2 and medfilt2. Examples demonstrate applying these techniques to enhance images.
Fuzzy sets allow for gradual membership of elements in a set, rather than binary membership as in classical set theory. Membership is described on a scale of 0 to 1 using a membership function. Fuzzy sets generalize classical sets by treating classical sets as special cases where membership values are restricted to 0 or 1. Fuzzy set theory can model imprecise or uncertain information and is used in domains like bioinformatics. Examples of fuzzy sets include sets like "tall people" where membership in the set is a matter of degree.
Morphological image processing uses small image patterns called structuring elements to probe and modify binary images. Basic morphological operations include erosion, dilation, opening, closing, and hit-or-miss transformation. Erosion shrinks objects and removes small details, while dilation expands objects and fills small holes. Opening performs erosion followed by dilation to smooth contours and break thin connections. Closing performs dilation followed by erosion to smooth contours but fuse breaks and fill holes. Hit-or-miss is used to detect specific shapes. Morphological operations have applications in boundary extraction, hole filling, thinning, thickening, and feature detection.
This document provides an overview of mathematical morphology and its applications to image processing. It discusses basic concepts like dilation, erosion, opening, closing and their properties. It also covers algorithms for tasks like boundary extraction, region filling, thinning and skeletonization. Grayscale morphology is introduced, including dilation, erosion and other operations on grayscale images. Some common applications are described, such as morphological smoothing, gradient calculation, top-hat transforms and textural segmentation.
The document discusses morphological image operations and mathematical morphology. It provides examples of basic morphological operations like dilation, erosion, opening and closing. It also discusses morphological algorithms for tasks like boundary extraction, region filling, connected component extraction, skeletonization, and using morphological operations for applications like detecting foreign objects. The key concepts covered are binary morphological operations, connectivity in images, and algorithms for thinning, boundary detection, and segmentation.
Mathematical morphology is a framework for image analysis using set theory operations. It is used for tasks like noise filtering, shape analysis, and segmentation. Basic operations include erosion, dilation, opening, and closing using a structuring element. Erosion shrinks objects while dilation expands them. Opening eliminates small objects and closing fills small holes. Together these operations can filter images while preserving overall shapes. Morphological operations also enable extracting object boundaries, thinning images to skeletons, and finding connected components.
The document discusses integration and indefinite integrals. It covers determining integrals by reversing differentiation, integrating algebraic expressions like constants, variables, and polynomials. It also discusses determining the constant of integration and using integration to find equations of curves from their gradients. Examples are provided to illustrate integrating functions and finding volumes generated by rotating an area about an axis.
The document discusses determining the location of the center of gravity, center of mass, and centroid of composite bodies, which are bodies made up of simpler shapes. It provides examples of how to use the method of moments to calculate the centroid by breaking the body into simpler parts, determining the properties of each part, and using equations that sum the weighted properties to find the total centroid. Students are expected to learn how to apply this method to find centroids of complex shapes by dividing them into simpler components.
Morphological image processing uses mathematical morphology operations to extract image components and analyze shapes. The key operations are dilation, erosion, opening, closing, and hit-and-miss transforms. Dilation expands object boundaries while erosion shrinks them. Opening performs erosion followed by dilation to remove noise, and closing performs dilation then erosion to fill gaps. Hit-and-miss transforms detect patterns by matching a structuring element. Together these operations can extract useful features and analyze shapes in binary images.
Morphological image processing uses basic set operations and structuring elements to extract image components and filter images. Erosion shrinks objects by removing pixels that don't match the structuring element, while dilation grows objects by adding pixels where the structuring element overlaps the object. Opening performs erosion followed by dilation to smooth contours and break thin connections, while closing performs dilation followed by erosion to fill in small holes and smooth contours. These operations can be used for tasks like filtering, boundary extraction, and region filling.
This document provides an overview of basic morphological image processing techniques. It defines morphological operations like dilation, erosion, opening and closing using set operations. Dilation expands objects and fills in holes while erosion shrinks objects. Boundary extraction is performed using erosion followed by a logical AND with the complement of the eroded image. Examples demonstrate using morphological operations to clean up a fingerprint image and extract an object from a noisy image.
This document describes spatial descriptions and transformations in robotics. It covers topics like coordinate frames, position and orientation descriptions, and various transformation methods between frames. Specifically, it discusses:
- Defining coordinate frames, position vectors, and rotation matrices to describe positions and orientations.
- Translation and rotation mappings to change descriptions between frames.
- Using Euler angles with the Z-YX/XYZ convention for rotating one frame to another with three successive rotations.
- The homogeneous transformation matrix for general transforms between frames with rotation and translation.
- Applications of rotation matrices, including inverting transformations.
1) The document describes developing the element matrix equation for a beam element with a uniformly distributed load. It involves discretizing the beam into elements, deriving the governing differential equation and boundary conditions for a general element, determining the shape functions through interpolation, and assembling the element stiffness matrix.
2) The weighted integral form of the governing differential equation is used to derive the element matrix equation. Shape functions are obtained as Hermite cubic polynomials.
3) As an example, the document analyzes a beam with two elements and applies the derived element matrix equation and boundary conditions to solve for displacements and forces.
Deflection of structures using double integration method, moment area method, elastic load method, conjugate beam method, virtual work, castiglianois second theorem and method of consistent deformations
Predictive model of moment of resistance for rectangular reinforced concrete ...Alexander Decker
This document presents a predictive model for calculating the moment of resistance (MR) for rectangular reinforced concrete sections. The model is developed based on stress-strain analysis of a singly reinforced concrete beam. The governing equation relates MR to the concrete compressive strength (fcu), breadth (b), and effective depth (d). Simulation results show that MR increases with larger b and d values. MR also increases at a higher rate with greater d due to its quadratic relationship in the equation, whereas the increase is linear with b. The model allows accurate selection of section dimensions for structural design based on required resistance.
1. This document contains a question bank on the topic of metrics spaces and topology. It includes 11 topics with multiple choice questions on concepts like metric spaces, open and closed sets, topological spaces, and examples of metric spaces like the real line and plane.
2. The questions assess understanding of fundamental topological concepts such as metrics, open and closed sets, topological spaces, and examples of specific topological spaces.
3. The document is a study guide containing practice questions to test comprehension of foundational topics in metric spaces and general topology.
1) The document provides instructions for a student's first assignment, which includes downloading course materials from the online course webpage and completing a homework assignment on the Webwork system.
2) It emphasizes that students should use Firefox to complete the Webwork homework, as other browsers like Safari and Internet Explorer may cause issues.
3) It also notes that claiming computer problems is not a valid excuse for missing homework, and students must use public computing sites if their own computer is not working.
490 students were willing to donate blood
340 students were willing to help serve breakfast
120 students were willing to do both
To find the number of students willing to donate blood or serve breakfast we take the union of these sets:
A = {students willing to donate blood} = 490
B = {students willing to serve breakfast} = 340
The number willing to do both is 120
Using the formula: |A ∪ B| = |A| + |B| - |A ∩ B|
|A ∪ B| = 490 + 340 - 120 = 710
Therefore, the number of students willing to donate blood or serve breakfast is 710.
This document discusses beam design criteria and deflection behavior of beams. It covers two key criteria for beam design:
1) Strength criterion - the beam cross section must be strong enough to resist bending moments and shear forces.
2) Stiffness criterion - the maximum deflection of the beam cannot exceed a limit and the beam must be stiff enough to resist deflections from loading.
It then defines deflection, slope, elastic curve, and flexural rigidity. It presents the differential equation that relates bending moment, slope, and deflection. Methods for calculating slope and deflection including double integration, Macaulay's method, and others are also summarized.
This document discusses line integrals and Green's theorem. It defines line integrals as integrals of scalar or vector fields along a curve, parameterized by arc length. Line integrals may depend on the path taken between two points, but are path-independent for conservative vector fields. Green's theorem relates line integrals around a closed curve to a double integral over the enclosed region, equating the line integral to the curl of the vector field integrated over the region. An example demonstrates using Green's theorem to evaluate a line integral as a double integral.
Use PyCharm for remote debugging of WSL on a Windo cf5c162d672e4e58b4dde5d797...shadow0702a
This document serves as a comprehensive step-by-step guide on how to effectively use PyCharm for remote debugging of the Windows Subsystem for Linux (WSL) on a local Windows machine. It meticulously outlines several critical steps in the process, starting with the crucial task of enabling permissions, followed by the installation and configuration of WSL.
The guide then proceeds to explain how to set up the SSH service within the WSL environment, an integral part of the process. Alongside this, it also provides detailed instructions on how to modify the inbound rules of the Windows firewall to facilitate the process, ensuring that there are no connectivity issues that could potentially hinder the debugging process.
The document further emphasizes on the importance of checking the connection between the Windows and WSL environments, providing instructions on how to ensure that the connection is optimal and ready for remote debugging.
It also offers an in-depth guide on how to configure the WSL interpreter and files within the PyCharm environment. This is essential for ensuring that the debugging process is set up correctly and that the program can be run effectively within the WSL terminal.
Additionally, the document provides guidance on how to set up breakpoints for debugging, a fundamental aspect of the debugging process which allows the developer to stop the execution of their code at certain points and inspect their program at those stages.
Finally, the document concludes by providing a link to a reference blog. This blog offers additional information and guidance on configuring the remote Python interpreter in PyCharm, providing the reader with a well-rounded understanding of the process.
Home security is of paramount importance in today's world, where we rely more on technology, home
security is crucial. Using technology to make homes safer and easier to control from anywhere is
important. Home security is important for the occupant’s safety. In this paper, we came up with a low cost,
AI based model home security system. The system has a user-friendly interface, allowing users to start
model training and face detection with simple keyboard commands. Our goal is to introduce an innovative
home security system using facial recognition technology. Unlike traditional systems, this system trains
and saves images of friends and family members. The system scans this folder to recognize familiar faces
and provides real-time monitoring. If an unfamiliar face is detected, it promptly sends an email alert,
ensuring a proactive response to potential security threats.
Software Engineering and Project Management - Introduction, Modeling Concepts...Prakhyath Rai
Introduction, Modeling Concepts and Class Modeling: What is Object orientation? What is OO development? OO Themes; Evidence for usefulness of OO development; OO modeling history. Modeling
as Design technique: Modeling, abstraction, The Three models. Class Modeling: Object and Class Concept, Link and associations concepts, Generalization and Inheritance, A sample class model, Navigation of class models, and UML diagrams
Building the Analysis Models: Requirement Analysis, Analysis Model Approaches, Data modeling Concepts, Object Oriented Analysis, Scenario-Based Modeling, Flow-Oriented Modeling, class Based Modeling, Creating a Behavioral Model.
Null Bangalore | Pentesters Approach to AWS IAMDivyanshu
#Abstract:
- Learn more about the real-world methods for auditing AWS IAM (Identity and Access Management) as a pentester. So let us proceed with a brief discussion of IAM as well as some typical misconfigurations and their potential exploits in order to reinforce the understanding of IAM security best practices.
- Gain actionable insights into AWS IAM policies and roles, using hands on approach.
#Prerequisites:
- Basic understanding of AWS services and architecture
- Familiarity with cloud security concepts
- Experience using the AWS Management Console or AWS CLI.
- For hands on lab create account on [killercoda.com](https://killercoda.com/cloudsecurity-scenario/)
# Scenario Covered:
- Basics of IAM in AWS
- Implementing IAM Policies with Least Privilege to Manage S3 Bucket
- Objective: Create an S3 bucket with least privilege IAM policy and validate access.
- Steps:
- Create S3 bucket.
- Attach least privilege policy to IAM user.
- Validate access.
- Exploiting IAM PassRole Misconfiguration
-Allows a user to pass a specific IAM role to an AWS service (ec2), typically used for service access delegation. Then exploit PassRole Misconfiguration granting unauthorized access to sensitive resources.
- Objective: Demonstrate how a PassRole misconfiguration can grant unauthorized access.
- Steps:
- Allow user to pass IAM role to EC2.
- Exploit misconfiguration for unauthorized access.
- Access sensitive resources.
- Exploiting IAM AssumeRole Misconfiguration with Overly Permissive Role
- An overly permissive IAM role configuration can lead to privilege escalation by creating a role with administrative privileges and allow a user to assume this role.
- Objective: Show how overly permissive IAM roles can lead to privilege escalation.
- Steps:
- Create role with administrative privileges.
- Allow user to assume the role.
- Perform administrative actions.
- Differentiation between PassRole vs AssumeRole
Try at [killercoda.com](https://killercoda.com/cloudsecurity-scenario/)
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Fluke Solar Application Specialist Will White is presenting on this engaging topic:
Will has worked in the renewable energy industry since 2005, first as an installer for a small east coast solar integrator before adding sales, design, and project management to his skillset. In 2022, Will joined Fluke as a solar application specialist, where he supports their renewable energy testing equipment like IV-curve tracers, electrical meters, and thermal imaging cameras. Experienced in wind power, solar thermal, energy storage, and all scales of PV, Will has primarily focused on residential and small commercial systems. He is passionate about implementing high-quality, code-compliant installation techniques.
2. 4/30/2021 2
Introduction
► Morphology: a branch of biology that deals with the form
and structure of animals and plants
► Morphological image processing is used to extract image
components for representation and description of region
shape, such as boundaries, skeletons, and the convex hull
3. 4/30/2021 3
Preliminaries (1)
► Reflection
► Translation
The reflection of a set , denoted , is defined as
{ | ,for }
B B
B w w b b B
1 2
The translation of a set by point ( , ), denoted ( ) ,
is defined as
( ) { | ,for }
Z
Z
B z z z B
B c c b z b B
7. 4/30/2021 7
Examples: Structuring Elements (2)
Accommodate the
entire structuring
elements when its
origin is on the
border of the
original set A
Origin of B visits
every element of A
At each location of
the origin of B, if B
is completely
contained in A,
then the location is
a member of the
new set, otherwise
it is not a member
of the new set.
8. 4/30/2021 8
Erosion
2
With and as sets in , the erosion of by , denoted ,
defined
| ( )Z
A B Z A B A B
A B z B A
The set of all points such that , translated by , is contained by .
z B z A
| ( ) c
Z
A B z B A
11. 4/30/2021 11
Dilation
2
With and as sets in , the dilation of by ,
denoted , is defined as
A B= |
z
A B Z A B
A B
z B A
The set of all displacements , the translated and
overlap by at least one element.
z B A
|
z
A B z B A A
14. 4/30/2021 14
Duality
► Erosion and dilation are duals of each other with respect to
set complementation and reflection
c c
c c
A B A B
and
A B A B
15. 4/30/2021 15
Duality
► Erosion and dilation are duals of each other with respect to
set complementation and reflection
|
|
|
c
c
Z
c
c
Z
c
Z
c
A B z B A
z B A
z B A
A B
16. 4/30/2021 16
Duality
► Erosion and dilation are duals of each other with respect to
set complementation and reflection
|
|
c
c
Z
c
Z
c
A B z B A
z B A
A B
17. 4/30/2021 17
Opening and Closing
► Opening generally smoothes the contour of an object,
breaks narrow isthmuses, and eliminates thin protrusions
► Closing tends to smooth sections of contours but it
generates fuses narrow breaks and long thin gulfs,
eliminates small holes, and fills gaps in the contour
18. 4/30/2021 18
Opening and Closing
The opening of set by structuring element ,
denoted , is defined as
A B
A B
A B A B B
The closing of set by structuring element ,
denoted , is defined as
A B
A B
A B A B B
19. 4/30/2021 19
Opening
The opening of set by structuring element ,
denoted , is defined as
|
Z Z
A B
A B
A B B B A
23. 4/30/2021 23
Duality of Opening and Closing
► Opening and closing are duals of each other with respect
to set complementation and reflection
( )
c c
A B A B
( )
c c
A B A B
24. 4/30/2021 24
The Properties of Opening and Closing
► Properties of Opening
► Properties of Closing
(a) is a subset (subimage) of
(b) if is a subset of , then is a subset of
(c) ( )
A B A
C D C B D B
A B B A B
(a) is subset (subimage) of
(b) If is a subset of , then is a subset of
(c) ( )
A A B
C D C B D B
A B B A B
26. 4/30/2021 26
The Hit-or-Miss
Transformation
if denotes the set composed of
and its background,the match
(or set of matches) of in ,
denoted ,
* c
B
D
B A
A B
A B A D A W D
1 2
1
2
1 2
,
:object
: background
( )
c
B B B
B
B
A B A B A B
27. 4/30/2021 27
Some Basic Morphological Algorithms (1)
► Boundary Extraction
The boundary of a set A, can be obtained by first eroding A
by B and then performing the set difference between A
and its erosion.
( )
A A A B
30. 4/30/2021 30
Some Basic Morphological Algorithms (2)
► Hole Filling
A hole may be defined as a background region surrounded
by a connected border of foreground pixels.
Let A denote a set whose elements are 8-connected
boundaries, each boundary enclosing a background region
(i.e., a hole). Given a point in each hole, the objective is to
fill all the holes with 1s.
31. 4/30/2021 31
Some Basic Morphological Algorithms (2)
► Hole Filling
1. Forming an array X0 of 0s (the same size as the array
containing A), except the locations in X0 corresponding to
the given point in each hole, which we set to 1.
2. Xk = (Xk-1 + B) Ac k=1,2,3,…
Stop the iteration if Xk = Xk-1
34. 4/30/2021 34
Some Basic Morphological Algorithms (3)
► Extraction of Connected Components
Central to many automated image analysis applications.
Let A be a set containing one or more connected
components, and form an array X0 (of the same size as the
array containing A) whose elements are 0s, except at each
location known to correspond to a point in each connected
component in A, which is set to 1.
35. 4/30/2021 35
Some Basic Morphological Algorithms (3)
► Extraction of Connected Components
Central to many automated image analysis applications.
1
-1
( )
:structuring element
until
k k
k k
X X B A
B
X X
38. 4/30/2021 38
Some Basic Morphological Algorithms (4)
► Convex Hull
A set A is said to be convex if the straight line segment
joining any two points in A lies entirely within A.
The convex hull H or of an arbitrary set S is the smallest
convex set containing S.
39. 4/30/2021 39
Some Basic Morphological Algorithms (4)
► Convex Hull
1
Let , 1, 2, 3, 4, represent the four structuring elements.
The procedure consists of implementing the equation:
( * )
1,2,3,4 and 1,
i
i i
k k
B i
X X B A
i k
0
1
4
1
2,3,...
with .
When the procedure converges, or ,let ,
the convex hull of A is
( )
i
i i i i
k k k
i
i
X A
X X D X
C A D
42. 4/30/2021 42
Some Basic Morphological Algorithms (5)
► Thinning
The thinning of a set A by a structuring element B, defined
( * )
( * )c
A B A A B
A A B
43. 4/30/2021 43
Some Basic Morphological Algorithms (5)
► A more useful expression for thinning A symmetrically is
based on a sequence of structuring elements:
1 2 3
-1
, , ,...,
where is a rotated version of
n
i i
B B B B B
B B
1 2
The thinning of by a sequence of structuring element { }
{ } ((...(( ) )...) )
n
A B
A B A B B B
45. 4/30/2021 45
Some Basic Morphological Algorithms (6)
► Thickening:
The thickening is defined by the expression
*
A B A A B
1 2
The thickening of by a sequence of structuring element { }
{ } ((...(( ) )...) )
n
A B
A B A B B B
In practice, the usual procedure is to thin the background of the set
and then complement the result.
47. 4/30/2021 47
Some Basic Morphological Algorithms (7)
► Skeletons
A skeleton, ( ) of a set has the following properties
a. if is a point of ( ) and ( ) is the largest disk
centered at and contained in , one cannot find a
larger disk containing ( )
z
z
S A A
z S A D
z A
D and included in .
The disk ( ) is called a maximum disk.
b. The disk ( ) touches the boundary of at two or
more different places.
z
z
A
D
D A
49. 4/30/2021 49
Some Basic Morphological Algorithms (7)
0
The skeleton of A can be expressed in terms of
erosion and openings.
( ) ( )
with max{ | };
( ) ( ) ( )
where is a structuring element, and
K
k
k
k
S A S A
K k A kB
S A A kB A kB B
B
( ) ((..(( ) ) ...) )
successive erosions of A.
A kB A B B B
k
52. 4/30/2021 52
Some Basic Morphological Algorithms (7)
0
A can be reconstructed from the subsets by using
( ( ) )
where ( ) denotes successive dilations of A.
( ( ) ) ((...(( ( ) ) )... )
K
k
k
k
k k
A S A kB
S A kB k
S A kB S A B B B
54. 4/30/2021 54
Some Basic Morphological Algorithms (8)
► Pruning
a. Thinning and skeletonizing tend to leave parasitic components
b. Pruning methods are essential complement to thinning and
skeletonizing procedures
60. 4/30/2021 60
Some Basic Morphological Algorithms (9)
► Morphological Reconstruction
It involves two images and a structuring element
a. One image contains the starting points for the
transformation (The image is called marker)
b. Another image (mask) constrains the transformation
c. The structuring element is used to define connectivity
61. 4/30/2021 61
Morphological Reconstruction: Geodesic
Dilation
(1)
(1)
Let denote the marker image and the mask image,
. The geodesic dilation of size 1 of the marker image
with respect to the mask, denoted by ( ), is defined as
( ) G
G
G
F G
F G
D F
D F F B
( )
( ) (1) ( 1)
(0)
The geodesic dilation of size of the marker image
with respect to , denoted by ( ), is defined as
( ) ( ) ( )
with ( ) .
n
G
n n
G G G
G
n F
G D F
D F D F D F
D F F
63. 4/30/2021 63
Morphological Reconstruction: Geodesic
Erosion
(1)
(1)
Let denote the marker image and the mask image.
The geodesic erosion of size 1 of the marker image with
respect to the mask, denoted by ( ), is defined as
( ) G
G
G
F G
E F
E F F B
( )
( ) (1) ( 1)
(0)
The geodesic erosion of size of the marker image
with respect to , denoted by ( ), is defined as
( ) ( ) ( )
with ( ) .
n
G
n n
G G G
G
n F
G E F
E F E F E F
E F F
65. 4/30/2021 65
Morphological Reconstruction by Dilation
Morphological reconstruction by dialtion of a mask image
from a marker image , denoted ( ), is defined as
the geodesic dilation of with respect to , iterated until
stability is achieved; that
D
G
G F R F
F G
( )
( ) ( 1)
is,
( ) ( )
with such that ( ) ( ).
D k
G G
k k
G G
R F D F
k D F D F
67. 4/30/2021 67
Morphological Reconstruction by Erosion
Morphological reconstruction by erosion of a mask image
from a marker image , denoted ( ), is defined as
the geodesic erosion of with respect to , iterated until
stability is achieved; that i
E
G
G F R F
F G
( )
( ) ( 1)
s,
( ) ( )
with such that ( ) ( ).
E k
G G
k k
G G
R F E F
k E F E F
68. 4/30/2021 68
Opening by Reconstruction
( )
The opening by reconstruction of size of an image is
defined as the reconstruction by dilation of from the
erosion of size of ; that is
( )
where
n D
R F
n F
F
n F
O F R F nB
F nB
indicates erosions of by .
n F B
70. 4/30/2021 70
Filling Holes
Let ( , ) denote a binary image and suppose that we
form a marker image that is 0 everywhere, except at
the image border, where it is set to 1- ; that is
1 ( , ) if ( , ) is on the bor
( , )
I x y
F
I
I x y x y
F x y
der of
0 otherwise
then
( )
c
c
D
I
I
H R F
73. 4/30/2021 73
Border Clearing
It can be used to screen images so that only complete objects
remain for further processing; it can be used as a singal that
partial objects are present in the field of view.
The original image is used as the mask and the following
marker image:
( , ) if ( , ) is on the border of
( , )
0 otherwise
I x y x y I
F x y
X I R
( )
D
I F
80. 4/30/2021 80
Gray-Scale Morphology: Erosion and Dilation
by Flat Structuring
( , )
( , )
( , ) min ( , )
( , ) max ( , )
s t b
s t b
f b x y f x s y t
f b x y f x s y t
82. 4/30/2021 82
Gray-Scale Morphology: Erosion and Dilation
by Nonflat Structuring
( , )
( , )
( , ) min ( , ) ( , )
( , ) max ( , ) ( , )
N N
s t b
N N
s t b
f b x y f x s y t b s t
f b x y f x s y t b s t
83. 4/30/2021 83
Duality: Erosion and Dilation
( , ) ( , )
where ( , ) and ( , )
c c
c
c c
f b x y f b x y
f f x y b b x y
f b f b
( )
c c
f b f b
84. 4/30/2021 84
Opening and Closing
f b f b b
f b f b b
c c
c c
f b f b f b
f b f b f b
86. 4/30/2021 86
Properties of Gray-scale Opening
1 2 1 2
( )
( ) if , then
( )
where denotes is a subset of and also
( , ) ( , ).
a f b f
b f f f b f b
c f b b f b
e r e r
e x y r x y
87. 4/30/2021 87
Properties of Gray-scale Closing
1 2 1 2
( )
( ) if , then
( )
a f f b
b f f f b f b
c f b b f b
89. 4/30/2021 89
Morphological Smoothing
► Opening suppresses bright details smaller than the
specified SE, and closing suppresses dark details.
► Opening and closing are used often in combination as
morphological filters for image smoothing and noise
removal.
91. 4/30/2021 91
Morphological Gradient
► Dilation and erosion can be used in combination with
image subtraction to obtain the morphological gradient of
an image, denoted by g,
► The edges are enhanced and the contribution of the
homogeneous areas are suppressed, thus producing a
“derivative-like” (gradient) effect.
( ) ( )
g f b f b
93. 4/30/2021 93
Top-hat and Bottom-hat Transformations
► The top-hat transformation of a grayscale image f is
defined as f minus its opening:
► The bottom-hat transformation of a grayscale image f is
defined as its closing minus f:
( ) ( )
hat
T f f f b
( ) ( )
hat
B f f b f
94. 4/30/2021 94
Top-hat and Bottom-hat Transformations
► One of the principal applications of these transformations
is in removing objects from an image by using structuring
element in the opening or closing operation
96. 4/30/2021 96
Granulometry
► Granulometry deals with determining the size of
distribution of particles in an image
► Opening operations of a particular size should have the
most effect on regions of the input image that contain
particles of similar size
► For each opening, the sum (surface area) of the pixel
values in the opening is computed
101. 4/30/2021 101
Gray-Scale Morphological Reconstruction (1)
► Let f and g denote the marker and mask image with the
same size, respectively and f ≤ g.
The geodesic dilation of size 1 of f with respect to g is
defined as
The geodesic dilation of size n of f with respect to g is
defined as
(1)
( )
where denotes the point-wise minimum operator.
g
D f f g g
( ) (1) ( 1) (0)
( ) ( ) with ( )
n n
g g g g
D f D D f D f f
102. 4/30/2021 102
Gray-Scale Morphological Reconstruction (2)
► The geodesic erosion of size 1 of f with respect to g is
defined as
The geodesic erosion of size n of f with respect to g is
defined as
(1)
( )
where denotes the point-wise maximum operator.
g
E f f g g
( ) (1) ( 1) (0)
( ) ( ) with ( )
n n
g g g g
E f E E f E f f
103. 4/30/2021 103
Gray-Scale Morphological Reconstruction (3)
► The morphological reconstruction by dilation of a gray-
scale mask image g by a gray-scale marker image f, is
defined as the geodesic dilation of f with respect to g,
iterated until stability is reached, that is,
The morphological reconstruction by erosion of g by f is
defined as
( )
( ) ( 1)
( )
with k such that
D k
g g
k k
g g
R f D f
D f D f
( )
( ) ( 1)
( )
with k such that
E k
g g
k k
g g
R f E f
E f E f
104. 4/30/2021 104
Gray-Scale Morphological Reconstruction (4)
► The opening by reconstruction of size n of an image f is
defined as the reconstruction by dilation of f from the
erosion of size n of f; that is,
The closing by reconstruction of size n of an image f is
defined as the reconstruction by erosion of f from the
dilation of size n of f; that is,
( )
( )
n D
R f
O f R f nb
( )
( )
n E
R f
C f R f nb
106. 4/30/2021 106
Steps in the Example
1. Opening by reconstruction of the original image using a horizontal
line of size 1x71 pixels in the erosion operation
2. Subtract the opening by reconstruction from original image
3. Opening by reconstruction of the f’ using a vertical line of size 11x1
pixels
4. Dilate f1 with a line SE of size 1x21, get f2.
( )
( )
n D
R f
O f R f nb
( )
' ( )
n
R
f f O f
( )
1 ( ') ' '
n D
R f
f O f R f nb
107. 4/30/2021 107
Steps in the Example
5. Calculate the minimum between the dilated image f2
and and f’, get f3.
6. By using f3 as a marker and the dilated image f2 as
the mask,
( )
2 2
( ) ( 1)
2 2
( 3) 3
with k such that 3 3
D k
f f
k k
f f
R f D f
D f D f