2: Image Display and Digital Images. EE547 Computer Vision: Lecture Slides. 2: Digital Images. 1. Introduction: EE547 Computer Vision

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1 EE547 Computer Vision: Lecture Slides Anthony P. Reeves November 24, 1998 Lecture 2: Image Display and Digital Images 2: Image Display and Digital Images Image Display: - True Color, Grey, Pseudo Color, Color LUT s Digital Images: - Gray levels, Resolution and Tessellation. Readings: Jain 2:25-60 Lecture 1: Introduction 1. Introduction: EE547 Computer Vision Course Overview Use the www for information ee547 1st half: fundamentals and fixed labs 2nd half: advanced topics and project What is Computer Vision? 1. Applications 2. Capabilites Image Sensors 1. Video camera (vidicon and CCD) 2. Scanners (light or camera) 3. Reconstruction from projections (CT,MR) 4. Range image sensing: (structured light, stereo, active (time-of-flight)) Readings: Jain Chapter 1:1-18, Chapter 2: : Digital Images Quantization (Number of gray levels): 8-12 bits typical Sampling (spatial frequency) Tessellation (Grid Pattern) Tessellation A plane can be tiled with three regular polygons: the triangle, the square and the hexagon. (a) Rectangular - Two types of connectivity: 4-connected and 8-connected - Local Distance problem 4-c = 1, 8-c = - Distance measures 1. Euclidean 2. City Block 3. Chess Board (b) Triangular Tessellation 1. Three types of connectivity 2. Not very useful for planar surfaces. Sometimes used for tessellating the surface of a sphere.

2 2: Digital Images 3: Moments: Size and Location (c) Hexagonal Tessellation 1. Only one type of connectivity 2. Cell indexing is more complicated than for the rectangular case. 3. Does not extend to three dimensions 4. Hexagonal tessellation my be achieved directly from a scanning imaging device. The two-dimensional Cartesian moment,, of order, of a density distribution function,, is defined as The two-dimensional moment for a, is discretized image, A complete moment set of order consists of all moments,, such that and contains elements. Note that the monomial product is the basis function for this moment definition. Size The size of a region is given by : Location The location of a region is given by its center of mass (COM) Lecture 3: Image Geometry and Algorithms 3: Image Geometry and Algorithm Types Image Geometry 1. The Perspective Transform: - How object points map into image points 2. Image Functions: - pixels and voxels. 3. Coordinate Systems: - Jain et. al., VisionX Image Algorithms: - Point, Local, Global, and Object. Binary Image Processing (Introduction) - Binary Image Formation: Thresholding Geometric Properties: Moments - Size, Location, Rotation Readings: Jain 2: : Moments (Rotation) Central Moments If the origin of the coordinate system is at the COM of the region; i.e.. ( ) and ( ), then the moments are referred to as central moments. Central moments are given by: where and. Rotation When the coordinate axis are aligned with principal axis of the region. The angle between the coordinate axis and the principle axis of the region is given by:

3 Lecture 4: Binary Image Processing 4: Binary Image Processing 5: VisionX Parameter Conventions Parameter Passing Conventions Image Algorithms: - Point, Local, Global, and Object. Image Formation: Thresholding Geometric Properties: Moments - Size, Location, Rotation Readings: Jain 2: All parameters have prefixes and are position independent Type Syntax Example option -[letter,name] -q value name = value maximum=100 file names name = fname of=outputfile input file if= fname if=image1 output file of= fname of=image2 output file -o fname -o image2 help -H -H help The -H option is defined for all VisionX commands and prints the commands syntax. 3. The - option is defined for all VisionX commands and prints the commands syntax and additional descriptive information. 4. If parameters are given without a prefix they satisfy value parameters (in the order given by -H). Lecture 5: VisionX and Binary Image Algorithms 5: VisionX and Binary Image Algorithms 5: VisionX Features VisionX commands can be used as UNIX filters The VisionX software package and Lab2 1. Command conventions 2. Data structures 3. Program example Binary Image Algorithms 1. Connected Component Labeling 2. Boundary Extraction Readings: Jain 2:25-60 Some commands are VisionX V3 (the old system) All new programs use VisionX V4 tools. VisionX V3 and VisonX file formats are different -VisionX V4 programs accept the main VisionX V3 formats -VisionX V3 programs accept simple VisionX V4 formats File name extensions can modify the file format Example:,o will make a VisionX V4 program create a VisionX V3 file

4 Lecture 6: Binary Image Algorithms II 6: Binary Image Algorithms II Lecture 7: Regions 7: Regions Connected Component Labeling Geometric Properties: Moments - Size, Location, Rotation Shape Description Medial Axis Transform: (Thinning) Readings: Jain 2:25-60 Local Operations (Convolution review) Local Operations (Binary Images) 1. Expanding, Shrinking 2. Dilation, Erosion 3. Opening (Erosion + Dilation), Closing (Dilation + Erosion) Automatic Threshold Selection 1. Peakiness Detection 2. Iterative Threshold Selection 3. Adaptive Thresholding Region Growing Readings: Jain 3: : Local Operations: (Convolution) 7: Morphological Operations: (Dilation) Convolution:See Jain 4: Dilation: is defined by: is defined by: For a discrete function where - the structuring element is a small binary valued matrix. Dilation may also be expressed by: Image Processing Local Operations Usually and are images - same size Border elements of may not be valid. - the convolution mask is a small matrix. convolution, correlation: Erosion: is defined by: Erosion gives all locations where a structuring element fits within a region.

5 Lecture 8: Segmentation 8: Segmentation Lecture 10: Image Filtering 10: Image Filtering II Morphological Filtering Opening (Erosion + Dilation), Closing (Dilation + Erosion) Region Representation 1. Array, Moments, Medial Axis 2. Quad Trees, Pyramids 3. Region Adjacency graphs, Supergrids (see book) Region Growing 1. Region Growing Criteria 2. Region Growing Order: Split and Merge, Boundary Melting Readings: Jain 3: Readings: Jain 4: Project Introduction The Fourier Transform 5. Sampling (digital images) Reconstruction by interpolation 6. The Discrete Fourier Transform (DFT) 7. Fourier Transforms and Convolution The Fast Fourier Transform (FFT) Practical issues Contrast Enhancement 1. Linear Scaling 2. Log Function 3. Histogram Equalization Readings: Jain 4: Lecture 9; Image Filtering: The Fourier Transform 9: Image Filtering: The Fourier Transform Split and Merge Region Growing Region merging by boundary melting The Fourier Transform 1. Review 2. Fourier Transform Pairs delta, comb, Gaussian, sin, cos, rect, sinc 3. Convolution 4. 2-D DFT Examples Readings: Jain 4: : Fourier Transform: Practical Issues 1. Arithmetic: complex numbers, large dynamic range - use floating point (or scaled fixed point with special hardware). 2. Fourier transform requires a large amount of computation - use the FFT algorithm (data size must be a power of 2) 3. Gibbs effect at the edges of an image (i) double the number of samples (a fix for convolution) (ii) taper the image to zero at the edges (frequency estimation) (ii) Use the discrete cosine transform (DCT) (image compression)

6 10: Image Enhancement vppr himage histeq -lin himage vppr histeq -log himage vppr histeq -lin himage of=himage.lin histeq -log himage.lin vppr histeq -equ himage vppr Lecture 12: Spatial Filtering Contrast Enhancement 1. Linear Scaling 2. Log Function 12: Spatial Filtering 3. Histogram Equalization Spatial Filtering High Pass and Low Pass Filters Linear Filtering (low pass) 1. The Mean filter Computational complexity - Separable - Update algorithm 2. Gaussian Smoothing - smooth in space and frequency - separable and rotationally symmetric Readings: Jain 4: Readings: Jain 5: Lecture 11: Image Filtering 11: Image Filtering Lecture 13: Edge Detection 13: Spatial Filtering and Edge Detection Fourier Transform: Practical Issues 1. Computation Complexity (FFT) 2. Gibbs Effect. Contrast Enhancement 1. Linear Scaling 2. Log Function Readings: Jain 4: Readings: Jain 5: Gaussian Smoothing - smooth in space and frequency - separable and rotationally symmetric High Pass Filtering Background Subtraction (Unsharp masking) Non-linear filtering (Median Filtering) Edge Detection Gradient Operators 1. Roberts Cross 2. Sobel 3. Prewitt Readings: Jain 5: , ,

7 Lecture 14: Edge Detection and Template Matching 14: Edge Detection and Template Matching Lecture 16: Curves and the Hough Transform 16: Curves and the Hough Transform Edge Detection (Lapalcian),Laplacian of the Gaussian Canny Edge Operator Nonmaxima Suppression Thresholding with Hysteresis Readings: Jain 5: , , Curves and Boundary Approximation Circular arc and Spline segments B-Splines (Cubic B-Splines) Cubic Splines B-Splines Reading: Jain 13: The Hough Transform 1. The Straight Line Hough Transform Readings: Jain 6: , , Lecture 15: Template Matching and Contour Representation 15: Template Matching and Contour Representation Lecture 17: The Hough Transform 17: The Hough Transform Template Matching Reading: Jain 15: Correlation 2. Cross Correlation 3. Normalized Correlation Contours Polylines Chain codes Curves 1. curve length 2. normal to a curve point 3. curvature of a curve point Readings: Jain 6: , , The Hough Transform 1. The Straight Line Hough Transform 2. The Parametric Hough Transform 3. The Generalized Hough Transform: Rotation Invariant GHT (RIGHT), R-tables, Reference point Readings: Jain 6: , ,

8 Lecture 18: Fourier Descriptors 18: Fourier Descriptors Lecture 19:Standard Moments and Object Recognition 19: Standard Moments and Object Recognition Fourier Descriptors: 1. Translation 2. Scale 3. Rotation (and starting point) 4. Normalization Readings: Jain 6: Readings: Jain 15: Standard Moments 1. Translation 2. Scale 3. Rotation 4. Reflection and Aspect Ratio 5. Image types: Binary, Grey and Range Object Recognition: An example Readings: Jain 6: Readings: Jain 15: : Global Features 19: Standard Moments 1. Template Matching Preprocessing:(a) none, (b) segment object from background. (c) edge operator Very sensitive to rotation and scale Identification: Threshold(peak detect) correlation image Other parameters: window size, matching criterion 2. Rotation Invariant Generalized Hough transform (RIGHT) Preprocessing: directed edge image Insensitive to rotation, sensitive to scale Occlusion: can handle some missing information Identification: Threshold(peak detect) accumulation image 3. Fourier Descriptors Preprocessing: whole closed contour Invariant to rotation and scale. Occlusion: Cannot handle missing contour information Identification: feature vector classification 4. Standard Moments Preprocessing:(a) none, (b) segment object from background. Invariant to rotation and scale. Occlusion: Cannot handle missing segment information Other features: can be used with grey level images and range images Moment Definition: The two-dimensional Cartesian moment,, of order, of a density distribution function,, is defined as The two-dimensional moment for a, is discretized image, A complete moment set of order consists of all moments,, such that and contains elements. Note that the monomial product is the basis function for this moment definition. Translation: A translation of in the dimension and in the dimension of an image,, results in a new image,, defined by The transformed moment values are expressed in terms of the original moment values of as

9 Scale: Rotation: 19: Standard Moments Lecture 20: Feature Vector Classification 20: Feature Vector Classification Statistical Classification: 1. Bayes Theorem 2. Discriminant Functions 3. Multivariate Gaussian Distributions 4. Linear Discriminant Functions The Nearest Neighbor Classifier Neural Networks Readings: Jain 15: Reflection: 19: Standard Moment Normalization Size: Location:, Rotation:,, Reflection: Aspect Ratio: Lecture 21: Classification and Neural Networks 21: Classification and Neural Networks The Nearest Neighbor Classifier Neural Networks 1. Perceptrons 2. Multi-layer Feed-forward Networks Object Recognition: An example Readings: Jain 15:

10 21: Classification Methods Linear Discriminant Functions Realize hyperplanes in decision space Multivariate Gaussian Distribution Parametric Classifier Gaussian shaped cluster assumption. Realizes hyperquadratic decision functions in hyperspace. In general, a large training set is required to estimate parameters. The Nearest Neighbor Classifier Problem: operation computation increases with size of training set. The K-Nearest Neighbor Classifier More robust version of Nearest Neighbor Classifier. Neural Networks: Perceptrons Implement hyperplanes in hyperspace Neural Networks: Multi-layer Feed-forward Networks Implement arbitrary complex decision surfaces in hyperspace with three layers. Issues: how many neurons in hidden layer, how to efficiently train, how to deal with contradictory training information. Lecture 23: Radiometry and Color 23: Radiometry and Color Radiometry Readings: Jain 9: Irradiance and Radiance 2. Reflectance, Bidirectional Reflectance Distribution Function (BRDF) 3. Surface types: Lambertian, Specular, Combination 4. Shape from Shading: Photometric Stereo Color Readings: Jain 10: Color coding schemes RGB, opponent processes, YIQ, IHS Depth Readings: Jain 11: Lecture 22: 3D Object Recognition Example 22: 3D Object Recognition Example Lecture 24: Depth etc. 24: Depth and Stereo Vision Object Recognition: An example 1. Multiple View Representation for Three-Dimensional Objects 2. Tessellation of the surface of a sphere 3. Feature Vector Conditioning: Variance Balancing, Aspect Ratio Normalization 4. Performance Evaluation 5. Other issues: The use of Range Information Confidence Estimation Multiple Camera Views Radiometry Readings: Jain 9: Color Readings: Jain 10: Depth Readings: Jain 11: Stereo Imaging 1. Perspective Projection Model 2. Stereo Geometry - Depth 3. Homogeneous Coordinates 4. 3D Rotations and Translations 5. Coordinate Systems 6. Disparity Computation Readings: Jain 15:

11 Lecture 25: Reconstruction from Projections 25: Reconstrcution from Projections Reconstruction from Projections 1. The Radon Transform 2. Simple Back Projection 3. The Fourier Transfrom Method 4. Filtered Back Projection Lecture 26: 3D Image Analysis 26: Bits and Pieces Prelim 2: Post Mortem The Final Project Report: Due December 3 The Project Poster: Setup by EARLY December 3 A 3-Dimensional Vision Application: Classifying Pulmonary Nodules from Helical CT Images 1. The Pulmonary Nodule Problem 2. 3D Image Filtering 3. 3D Shape Characterization 4. 3D Shape Classification

Digital Image Processing

Digital Image Processing Third Edition Rafael C. Gonzalez University of Tennessee Richard E. Woods MedData Interactive PEARSON Prentice Hall Pearson Education International Contents Preface xv Acknowledgments