Digital image processing: an algorithmic introduction
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| Main Authors: | , |
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| Format: | Book |
| Language: | English |
| Published: |
Cham, Switzerland
Springer
[2022]
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| Edition: | Third edition |
| Series: | Texts in computer science
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | XXV, 943 Seiten Illustrationen, Diagramme |
| ISBN: | 9783031057434 |
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MARC
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| 245 | 1 | 0 | |a Digital image processing |b an algorithmic introduction |c Wilhelm Burger, Mark J. Burge |
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| 650 | 4 | |a Computational intelligence | |
| 650 | 4 | |a Image Processing and Computer Vision | |
| 650 | 4 | |a Signal, Image and Speech Processing | |
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Contents Part I Images and Pixels 1 Digital Images. 1.1 Programming with Images. 1.2 1.3 1.4 1.5 1.6 1.7 1.8 2 Image Analysis and Computer Vision. Types of Digital Images . Image Acquisition. 1.4.1 The Pinhole Camera Model. 1.4.2 The “Thin” Lens . 1.4.3 Going Digital . 1.4.4 Image Size and Resolution. 1.4.5 Image Coordinate System. 1.4.6 Pixel Values. Image File Formats . 1.5.1 Raster Versus Vector Data. 1.5.2 Tagged Image File Format (TIFF). 1.5.3 Graphics Interchange Format (GIF). 1.5.4 Portable Network Graphics (PNG). 1.5.5 JPEG. 1.5.6 Legacy File Formats . 1.5.7 Bits and Bytes. Software for Digital Imaging . ImageJ. 1.7.1 Key Features. 1.7.2 Interactive
Tools. 1.7.3 Working With ImageJ and Java. Exercises . Histograms and Image Statistics. 2.1 What is a Histogram?. 2.2 Interpreting Histograms . 2.2.1 Image Acquisition. 2.2.2 Image Defects. 2.3 Calculating Histograms. 2.4 Histograms of Images With More Than 8 Bits. 2.4.1 Binning . 2.4.2 Example. 2.4.3 Implementation. 2.5 Histograms of Color Images. 2.5.1 Intensity Histograms. 2.5.2 Individual Color Channel Histograms. 2.5.3 Combined Color Histograms . 3 4 4 6 6 6 8 9 10 11 11 13 14 14 15 16 16 20 21 23 23 24 25 25 27 29 30 31 31 33 36 37 37 37 38 38 39 39 40 XI
The Cumulative Histogram . Statistical Information from the Histogram. 2.7.1 Mean and Variance . 2.7.2 Median. 2.8 Block Statistics. 2.8.1 Integral Images. 2.8.2 Mean Intensity. 2.8.3 Variance. 2.8.4 Practical Calculation of Integral Images . 2.9 Exercises . Contents 2.6 2.7 3 41 41 42 43 43 43 45 45 45 46 Point Operations . 49 3.1 Modifying Image Intensity. 50 3.1.1 Contrast and Brightness. . 50 3.1.2 Limiting Values by Clamping. 50 3.1.3 Inverting Images. 51 3.1.4 Thresholding Operation. 51 3.2 Point Operations and Histograms. 51 3.3 Automatic Contrast Adjustment. 52 3.4 ·. Modified Auto-Contrast Operation. 54 3.5 Histogram Equalization. 55 3.6 Histogram Specification. 58 3.6.1 Frequencies and
Probabilities. 58 3.6.2 Principle of Histogram Specification. 59 3.6.3 Adjusting to a Piecewise Linear Distribution 60 3.6.4 Adjusting to a Given Histogram (Histogram Matching) . 61 3.6.5 Examples. 63 3.7 Gamma Correction. 67 3.7.1 Why “Gamma”?. 68 3.7.2 Mathematical Definition. 68 3.7.3 Real Gamma Values . 69 3.7.4 Applications of Gamma Correction. 70 3.7.5 Implementation. 71 3.7.6 Modified Gamma Correction. 71 3.8 Point Operations in Imaged. 74 3.8.1 Point Operations with Lookup Tables. 74 3.8.2 Arithmetic Operations . 75 3.8.3 Point Operations Involving Multiple Images . 75 3.8.4 Methods for Point Operations on Two Images 76 3.8.5 ImageJ Plugins Involving Multiple Images . . 76 3.9 Exercises . 77 Part II Filters, Edges and Corners 4 XII Filters. 4.1 What is a Filter? . 4.2 Linear Filters . 4.2.1 The Filter Kernel. 4.2.2
Applying the Filter . 4.2.3 Implementing Filter Operations . 4.2.4 Filter Plugin Examples. 85 85 87 87 87 88 89
4.2.5 Integer Coefficients. 4.2.6 Filters of Arbitrary Size. 4.2.7 Types of Linear Filters. Formal Properties of Linear Filters. 4.3.1 Linear Convolution . 4.3.2 Formal Properties of Linear Convolution . 4.3.3 Separability of Linear Filters. 4.3.4 Impulse Response of a Filter. Nonlinear Filters. 4.4.1 Minimum and Maximum Filters. 4.4.2 Median Filter. 4.4.3 Weighted Median Filter . 4.4.4 Other Nonlinear Filters. Implementing Filters. 4.5.1 Efficiency of Filter Programs. 4.5.2 Handling Image Borders·. 4.5.3 Debugging Filter Programs . Filter Operations in ImageJ. 4.6.1 Linear Filters . 4.6.2 Gaussian Filters. 4.6.3 Nonlinear Filters . Exercises . 91 92 92 95 96 96 98 99 100 101 103 105 107 108 108 109 110 Ill Ill 112 112 113 5 Edges and Contours. 5.1 What Makes an
Edge?. 5.2 Gradient-Based Edge Detection. 5.2.1 Partial Derivatives and the Gradient . 5.2.2 Derivative Filters. 5.3 Simple Edge Operators. 5.3.1 Prewitt and Sobel Edge Operators. 5.3.2 Roberts Edge Operator. 5.3.3 Compass Operators. 5.3.4 Edge Operators in ImageJ. 5.4 Other Edge Operators. 5.4.1 Edge Detection Based on SecondDerivatives 5.4.2 Edges at Different Scales . 5.4.3 From Edges to Contours. 5.5 Canny Edge Operator. 5.5.1 Preprocessing. 5.5.2 Edge Localization. 5.5.3 Edge Tracing and Hysteresis Thresholding . . 5.5.4 Additional Information. 5.5.5 Implementation. 5.6 Edge Sharpening. 5.6.1 Edge Sharpening with the Laplacian Filter . . 5.6.2 Unsharp Masking. 5.7 Exercises . . 117 117 118 119 119 120 121 124 124 126 126 126 126 127 128 130 130 131 133 134 134 135 137 142 6 Corner
Detection. 6.1 Points of Interest. 6.2 Harris Corner Detector. 6.2.1 The Local Structure Matrix. 145 145 146 146 4.3 4.4 4.5 4.6 4.7 contents XIII
Contents 6.3 6.4 6.5 6.6 6.2.2 Significance of the Local Structure Matrix . 6.2.3 Corner Response Function (CRF). 6.2.4 Selecting Corner Points. 6.2.5 Examples. Alternative Formulations . 6.3.1 Shi-Tomasi Corner Score. 6.3.2 MOPS Corner Score . Basic Implementation . 6.4.1 Summary. Sub-Pixel Corner Positions. 6.5.1 Position Interpolation by Second-Order Taylor Expansion. 6.5.2 Sub-Pixel Positioning Example. Exercises . 147 150 150 152 152 152 154 154 160 161 161 162 163 Part III Binary Images 7 Morphological Filters. 7.1 Shrink and Let Grow. 7.1.1 Pixel Neighborhoods. 7.2 Basic Morphological Operations. 7.2.1 The Structuring Element. 7.2.2 Point Sets . 7.2.3 Dilation. 7.2.4 Erosion. 7.2.5 Formal Properties of
Dilation and Erosion . 7.2.6 Designing Morphological Filters. 7.2.7 Application Example: Outline. 7.3 Composite Morphological Operations. 7.3.1 Opening. 7.3.2 Closing. 7.3.3 Properties of Opening and Closing. 7.4 Thinning (Skeletonization). 7.4.1 Basic Algorithm. 7.4.2 Fast Thinning Algorithm. 7.4.3 Java Implementation. 7.4.4 Built-in Morphological Operations in Imaged 7.5 Grayscale Morphology. 7.5.1 Structuring Elements. 7.5.2 Dilation and Erosion. 7.5.3 Grayscale Opening and Closing. 7.6 Exercises . 8 Regions in Binary Images. 8.1 8.2 XIV 167 168 169 170 170 170 171 171 172 173 176 177 177 179 179 180 180 181 185 186 187 187 188 188 189 195 Finding Connected Image Regions. 196 8.1.1 Region Labeling by Flood Filling. 196 8.1.2 Sequential Region Segmentation. 201 8.1.3 Region Labeling - Summary. 205 Region Contours. 206
8.2.1 Outer and Inner Contours. 206 8.2.2 Combining Region Labeling andContour Detection. 207
8.2.3 Java Implementation. Representing Image Regions. 8.3.1 Matrix Representation. 8.3.2 Run Length Encoding. 8.3.3 Chain Codes. 8.4 Properties of Binary Regions. 8.4.1 Shape Features. 8.4.2 Geometric Features. 8.5 Statistical Shape Properties. 8.5.1 Centroid. 8.5.2 Moments. 8.5.3 Central Moments. 8.5.4 Normalized Central Moments . 8.5.5 Java Implementation. 8.6 Moment-Based Geometric Properties. 8.6.1 Orientation. .·. 8.6.2 Region Eccentricity. 8.6.3 Equivalent Ellipse. 8.6.4 Bounding Box Aligned to the Major Axis . . 8.6.5 Invariant Region Moments. 8.7 Projections. 8.8 Topological Region Properties. 8.9 Java Implementation. 8.10 Exercises
. 8.3 9 210 Contents 212 212 213 213 216 217 217 220 220 221 221 222 222 223 223 224 226 226 227 232 233 234 234 Automatic Thresholding. 241 9.1 Global Histogram-Based Thresholding. 241 9.1.1 Image Statistics from the Histogram. 243 9.1.2 Simple Threshold Selection. 244 9.1.3 Iterative Threshold Selection (Isodata Algorithm). 246 9.1.4 Otsu’s Method. 248 9.1.5 Maximum Entropy Thresholding. 251 9.1.6 Minimum Error Thresholding. 254 9.2 Local Adaptive Thresholding. 261 9.2.1 Bernsen’s Method. 262 9.3 9.4 9.5 9.2.2 Niblack’s Method. 264 Java Implementation. 273 9.3.1 Global Thresholding Methods. 274 9.3.2 Adaptive Thresholding. 275 Summary and Further Reading. 275 Exercises . 276 Part IV Geometric Primitives 281 281 Slope-Intercept Form. 281 Parametric (Point-Vector) Form. 282 Algebraic Form. 282 Hessian Normal
Form. 284 Lines to Points Sets. 284 10 Fitting Straight Lines. 10.1 Straight Line Equations . 10.1.1 10.1.2 10.1.3 10.1.4 10.2 Fitting XV
10.2.1 Linear Regression. 10.2.2 Orthogonal Regression . 10.3 Example: Contour Segmentation. 10.4 Java Implementation. 10.5 Exercises . Contents 11 285 286 290 292 295 297 Fitting Circles. 297 11.1.1 Circle Equations. 297 11.1.2 Algebraic Circle Fits. 298 11.1.3 Geometric Circle Fitting. 305 11.2 Fitting Ellipses. 313 11.2.1 Algebraic Ellipse Fitting. 314 11.2.2 Geometric Ellipse Fitting. . 323 11.2.3 Orthogonal Distance Approximations. 331 11.3 Java Implementation. 337 11.3.1 Circle Fitting . 338 11.3.2 Ellipse Fitting. 338 Fitting Circles and Ellipses. 11.1 12 Defecting Geometric Primitives . 12.1 Random Sample Consensus (RANSAC). 12.1.1 How Many Random Draws Are Needed? . 12.1.2 RANSAC Line Detection Algorithm. 12.1.3 Detecting Multiple Lines. 12.1.4 RANSAC Circle
Detection. 12.1.5 RANDSAC Ellipse Detection. 12.1.6 RANSAC Extensions and Applications. 12.2 The Hough Transform. 12.2.1 Parameter Space. 12.2.2 Accumulator Map. 12.2.3 A Better Line Representation. 12.2.4 Hough Algorithm. 12.2.5 Hough Transform Extensions. 12.2.6 Hough Transform for Circles and Arcs. 12.2.7 Hough Transform for Ellipses. 12.3 Java Implementation. 12.4 Exercises . 341 343 344 345 346 348 352 355 355 356 357 357 359 363 366 369 369 370 Part V Color 13 XVI Color Images. 13.1 RGB Color Images. 13.1.1 Structure of Color Images. 13.1.2 Color Images in ImageJ . 13.2 Color Spaces and Color Conversion. 13.2.1 Conversion to Grayscale. :. 13.2.2 Desaturating RGB Color Images. 13.2.3 HSV/HSB and HLS Color Spaces. 13.2.4 TV Component Color Spaces: YUV, YIQ, and YCt,Cr. 13.2.5 Color Spaces for Printing: CMY
and CMYK 13.3 Statistics of Color Images. 375 375 376 379 387 387 389 389 400 403 406
13.3.1 How Many Different Colors Are in an Image? 13.3.2 Color Histograms. 13.4 Color Quantization. 13.4.1 Scalar Color Quantization . 13.4.2 Vector Quantization. 13.4.3 Java Implementation. 13.5 Exercises . 14 Colorimetric Color Spaces. 14.1 14.2 14.3 14.4 14.5 14.6 14.7 14.8 CIE Color Spaces. 14.1.1 CIE XYZ Color Space. 14.1.2 CIE x, y Chromaticity. 14.1.3 Standard Illuminants. 14.1.4 Gamut. 14.1.5 Variants of the CIE Color Space. CIELAB Color Space. :. 14.2.1 CIEXYZ - CIELAB Conversion. 14.2.2 CIELAB CIEXYZ Conversion. CIELUV Color Space. 14.3.1 CIEXYZ - CIELUV Conversion. 14.3.2 CIELUV^ CIEXYZ Conversion. 14.3.3 Measuring Color Differences. Standard RGB (sRGB). 14.4.1 Linear vs. Nonlinear Color Components . 14.4.2 CIEXYZ - sRGB Conversion. 14.4.3 sRGB —»
CIEXYZ Conversion. 14.4.4 Calculations with Nonlinear sRGB Values. Adobe RGB. Chromatic Adaptation. . 14.6.1 XYZ Scaling. 14.6.2 Bradford Color Adaptation . Colorimetric Support in Java. 14.7.1 Profile Connection Space (PCS) . 14.7.2 Color-Related Java Classes. 14.7.3 Implementation of the CIELAB Color Space (Example). 445 14.7.4 ICC Profiles. Exercises . 15 Filters for Color Images. 15.1 15.2 15.3 15.4 15.5 Linear Filters . 15.1.1 Monochromatic Application of Linear Filters 15.1.2 Color Space Matters . 15.1.3 Linear Filtering with Circular Values. Nonlinear Color Filters. 15.2.1 Scalar Median Filter. 15.2.2 Vector Median Filter. 15.2.3 Sharpening Vector Median Filter. Java Implementation. . Further Reading. Exercises
. 406 Contents 407 408 410 412 419 419 425 425 426 426 428 429 429 430 430 431 432 432 433 434 434 435 436 436 437 438 439 439 440 442 442 444 446 448 451 451 452 454 458 462 462 462 466 469 471 472 XVII
Contents 475 476 478 480 16.2.2 The Jacobian Matrix. 481 16.2.3 Squared Local Contrast. 482 16.2.4 Color Edge Magnitude . 483 16.2.5 Color Edge Orientation. 485 16.2.6 Grayscale Gradients Revisited. 486 Canny Edge Detector for Color Images. 489 Other Color Edge Operators . 493 Java Implementation. 494 Exercises . 494 1θ Edge Detection in Color Images. 16.1 Monochromatic Techniques . 16.2 Edges in Vector-Valued Images. 16.2.1 Multi-Dimensional Gradients. 16.3 16.4 16.5 16.6 17 Edge-Preserving Smoothing Filters. 17.1 17.2 17.3 17.4 17.5 Kuwahara-Type Filters. 17.1.1 Application to Color Images. Bilateral Filter. 17.2.1 Domain Filter. 17.2.2 Range Filter. 17.2.3 Bilateral Filter: General Idea. 17.2.4 Bilateral Filter with Gaussian Kernels. 17.2.5 Application to Color Images. 17.2.6 Efficient
Implementation by x/ySeparation . 17.2.7 Further Reading. . . Anisotropic Diffusion Filters. 17.3.1 Homogeneous Diffusion and the Heat Equation. 17.3.2 The Perona-Malik Filter. 17.3.3 Perona-Malik Filter for Color Images. 17.3.4 Geometry Preserving AnisotropicDiffusion. 17.3.5 Tschumperlé-Deriche Algorithm . Java Implementation. Exercises . 497 498 500 504 504 505 505 507 508 512 514 517 518 520 522 526 528 532 535 Part VI Spectral Techniques 539 18.1 The Fourier Transform . 540 18.1.1 Sine and Cosine Functions. 540 18.1.2 Fourier Series Representation of Periodic Functions. 543 18.1.3 Fourier Integral. 543 18.1.4 Fourier Spectrum and Transformation. 544 18.1.5 Fourier Transform Pairs. 545 18.1.6 Important Properties of the Fourier Transform 546 18.2 Working with Discrete Signals. 550 18.2.1 Sampling. 550 18.2.2 Discrete and Periodic Functions. 555 18.3 The Discrete Fourier Transform (DFT). 555 18.3.1 Definition of the
DFT. 557 18.3.2 Discrete Basis Functions. 558 18 Introduction to Spectral Methods. XVIII
18.3.3 Aliasing Again!. 18.3.4 Units in Signal and Frequency Space. 18.3.5 Power Spectrum. 18.4 Implementing the DFT. 18.4.1 Direct Implementation . 18.4.2 Fast Fourier Transform (FFT). 18.5 Exercises . 559 CONTENTS 562 563 563 563 565 565 567 567 19.1.1 2D Basis Functions . 567 19.1.2 Implementing the 2D DFT. 568 Visualizing the 2D Fourier Transform. 570 19.2.1 Range of Spectral Values . 571 19.2.2 Centered Representation of the DFT Spectrum.-. 571 Frequencies and Orientation in 2D. 572 19.3.1 Effective Frequency. 572 19.3.2 Frequency Limits and Aliasingin 2D. 573 19.3.3 Orientation. 574 19.3.4 Normalizing the Geometry of the 2D Spectrum. 574 19.3.5 Effects of Periodicity. 575 19.3.6 Windowing . 575 19.3.7 Common Windowing Functions. 577 2D Fourier Transform Examples. 581 Applications of the
DFT. 581 19.5.1 Linear Filter Operations in Frequency Space 582 19.5.2 Linear Convolution and Correlation. 585 19.5.3 Inverse Filters. 585 Exercises . 586 19 The Discrete Fourier Transform in 2D. 19.1 Definition of the 2D DFT. 19.2 19.3 19.4 19.5 19.6 20 The Discrete Cosine Transform (DCT) . 20.1 20.2 20.3 20.4 20.5 One-Dimensional DCT . 20.1.1 DCT Basis Functions. 20.1.2 Implementing the ID DCT. Two-Dimensional DCT. 20.2.1 Examples. 20.2.2 Separability. Java Implementation. Other Spectral Transforms. Exercises . 589 590 590 591 592 593 593 595 596 597 Part VII Image Transformations 21 Geometric Operations. 21.1 Coordinate Transformations in 2D. 21.1.1 Linear Coordinate Transformations. 21.1.2 Homogeneous Coordinates. 21.1.3 Affine (Three-Point) Mapping. 21.1.4
Projective (Four-Point) Mapping . 21.1.5 Bilinear Mapping. 601 602 603 603 605 608 614 XIX
Contents 21.1.6 Log-Polar Mapping . 615 21.1.7 Other Nonlinear Transformations. 620 21.1.8 Piecewise Image Transformations. 623 21.2 Resampling the Image. 624 21.2.1 Source-to-Target Mapping. 625 21.2.2 Target-to-Source Mapping. 626 21.3 Java Implementation. 627 21.3.1 Geometric Transformations. 627 21.3.2 Image Transformations. 629 21.3.3 Examples. 630 21.4 Exercises . 632 22 Pixel Interpolation . 22.1 22.2 22.3 22., 22.5 22.6 22.7 22.8 Interpolation in ID: Simple Methods . . 22.1.1 Nearest-Neighbor Interpolation. 22.1.2 Linear Interpolation. 22.1.3 Ideal Low-Pass Filter. Interpolation by Convolution. Cubic Interpolation. 4 Spline Interpolation. 22.4.1 Catmull-Rom Interpolation. 22.4.2 Cubic B-spline Approximation. 22.4.3 Mitchell-Netravali Approximation . 22.4.4 Lanczos
Interpolation. Interpolation in 2D . 22.5.1 Nearest-Neighbor Interpolation in 2D . 22.5.2 Bilinear Interpolation . 22.5.3 Bicubic and Spline Interpolation in 2D. 22.5.4 Lanczos Interpolation in 2D. 22.5.5 Examples and Discussion. Aliasing . 22.6.1 Sampling the Interpolated Image. 22.6.2 Space-Variant Low-Pass Filtering. Java Implementation. Exercises . 639 639 639 640 640 643 644 645 646 647 647 648 649 651 651 652 654 655 657 657 659 660 661 Part VIII Image Matching 23 Image Matching and Registration. 667 23.1 Template Matching in Intensity Images. 23.1.1 Distance between Image Patterns. 23.1.2 Matching Under Rotation and Scaling. 23.1.3 Java Implementation. 23.2 Matching Binary Images. 23.2.1 Direct Comparison of Binary Images. 23.2.2 The Distance Transform. . 23.2.3 Chamfer Matching. 23.2.4 Java Implementation. 23.3 Exercises
. 668 668 675 676 676 677 678 682 684 684 24 Non-Rigid Image Matching. 687 XX 24.1 The Lucas-Kanade Technique. 687
24.2 24.3 24.4 24.5 24.6 24.7 24.1.1 Registration in ID. 24.1.2 Extension to Multi-Dimensional Functions . The Lucas-Kanade Algorithm. 24.2.1 Summary of the Algorithm. Inverse Compositional Algorithm . Linear Transformation Parameters. 24.4.1 Pure Translation. 24.4.2 Affine Transformation. 24.4.3 Projective Transformation . 24.4.4 Concatenating Linear Transformations . 24.4.5 Coordinate Frames. Example. Java Implementation. Exercises . 687 Contents 689 690 693 694 698 698 699 701 701 702 702 704 704 Part IX Local Features 709 710 25.1.1 The LoG Filter. 710 25.1.2 Gaussian Scale Space. 715 25.1.3 LoG/DoG Scale Space. 718 25.1.4 Hierarchical Scale Space. 720 25.1.5 Scale Space Structure in SIFT. 724 Key Point Selection and Refinement. 730 25.2.1 Local Extrema Detection. 730 25.2.2 Position Refinement. 732 25.2.3
Suppressing Responses to Edge-Like Structures. 734 Creating Local Descriptors. 736 25.3.1 Finding Dominant Orientations. 737 25.3.2 SIFT Descriptor Construction. 740 SIFT Algorithm Summary. 747 Matching SIFT Features. 748 25.5.1 Feature Distance and Match Quality. 748 25.5.2 Examples. 753 Efficient Feature Matching. 756 Java Implementation. 759 25.7.1 SIFT Feature Extraction . 760 25.7.2 SIFT Feature Matching. 762 Exercises . 763 25 Scale-Invariant Feature Transform (SIFT). 25.1 Interest Points at Multiple Scales. 25.2 25.3 25.4 25.5 25.6 25.7 25.8 765 766 26.2 Building the Component Tree. 768 26.2.1 Component Tree Algorithms. 768 26.2.2 Component Tree Algorithm 1: Global Immersion. 770 26.2.3 Component Tree Algorithm 2: Local Flooding 774 26.2.4 Component Tree Examples. 777 26.3 Extracting MSERs from the Component Tree . 778 26.3.1 Component Size Variation (Growth Rate). 779 26 Maximally Stable Extremal Regions
(MSER). 26.1 Threshold Sets and Extremal Regions. XXI
26.3.2 Maximally Stable Components. 26.3.3 Constraints on Component Size and Diversity 26.3.4 MSER Feature Statistics and Equivalent Ellipse . 26.3.5 Additional Constraints . 26.3.6 Detecting Dark And Bright Blobs. 26.3.7 MSER Examples . 26.4 Matching MSERs. 26.5 Local Affine Frames. 26.6 Summary. Contents 781 781 784 785 787 788 789 792 794 Appendix A В Mathematical Symbols and Notation. 799 A.l Symbols. A. 2 Sets. A.2.1 Basic Set Symbols and Operators. A.2.2 Destructive Set Operators . A.2.3 Relations, Mappings and Functions. A.3, Sequences. A.3.1 Adding and Removing Elements. A.3.2 “Stack”-Type Sequences. A.3.3 “Queue”-Type Sequences . A.3.4 Sorting Sequences. A.4 Tuples and Objects . A.4.1 Type Definition and Instantiation. A.4.2 Accessing Object
Components. A.4.3 Duplication. A.5 Complex Numbers. 799 803 803 804 804 805 805 805 806 806 806 806 807 807 807 Linear Algebra . 809 B.l B.2 B.3 B.4 B.5 В.6 B.7 XXII Vectors and Matrices. B.l.l Column and Row Vectors. B.l.2 Extracting Submatrices andVectors. B.1.3 Length (Norm) of a Vector. Matrix Multiplication . B.2.1 Scalar Multiplication. B.2.2 Product of Two Matrices . B.2.3 Matrix-Vector Products. Vector Products. B.3.1 Dot (Scalar) Product. B.3.2 Outer Product . B.3.3 Cross Product. Trace and Determinant of a Square Matrix. Eigenvalues and Eigenvectors. B.5.1 Calculating Eigenvalues . B.5.2 Generalized Symmetric Eigenproblems. Homogeneous Coordinates. Basic Matrix-Vector Operations with the Apache Commons Math Library. B.7.1 Vectors and
Matrices. B.7.2 Matrix-Vector Multiplication. 809 810 811 811 811 811 812 812 813 813 814 814 814 815 816 818 819 820 821 821
B.8 В.7.3 Vector Products. 821 Contents В.7.4 Inverse of a Square Matrix. 822 B.7.5 Eigenvalues and Eigenvectors. 822 Solving Systems of Linear Equations . 822 B.8.1 Exact Solutions. 823 B.8.2 Over-Determined System (Least-Squares Solutions). 824 B.8.3 Solving Homogeneous Linear Systems . 825 C Nonlinear Least Squares. C.l Nonlinear Least-Squares Fitting . C.2 Solution Methods. C.2.1 Implementation With Apache Commons Math C.2.2 Example 1: One-Dimensional Curve Fitting . C.3 Multi-Dimensional NLS Problems. C.3.1 Example 2: Geometric Circle Fitting. C.3.2 Numerical Estimation of Partial Derivatives . 827 827 828 829 829 832 832 836 D Elements from Calculus. D.l Scalar and Vector Fields. D.l.l The Jacobian Matrix. D.l.2 Gradients. D.1.3 Maximum Gradient Direction. D.l.4 Divergence of a Vector Field . D.l.5 The Laplacian Operator. D.l.6 The Hessian Matrix. D.2 Taylor Series Expansion
. D.2.1 Single-Variable Functions. D.2.2 Multi-Variable Functions . D.2.3 Finding Function Extrema by 2nd-Order Taylor Expansion. 844 D.3 Estimating Derivatives of Discrete Functions. D.3.1 First-order Derivatives . D.3.2 Second-Order Derivatives. D.3.3 Alternative Formulations . 837 837 837 838 839 839 839 840 841 841 842 Sub-Pixel Maximum Finding. E.l Second-Order Interpolation in ID. E.2 Subpixel Interpolation in 2D. E.2.1 Quadratic Functions in 2D. E.2.2 Method A: Second-Order Taylor Interpolation E.2.3 Method B: Least-Squares Quadratic Interpolation . 855 E.2.4 Quartic Interpolation. 849 849 851 852 853 Geometry . F.l Straight Lines . . F.l.l Conversions Between Different Line Equations F.l.2 Intersectionsof Algebraic Lines. F.1.3 Intersections of Lines in Hessian Normal Form F.l.4 Numeric Line Fitting Examples. F.2 Circles . 861 861 861 863 863 863 865 E F 847 847 848 848 857 XXIII
F.2.1 Circle Equations and Conversions. F.2.2 Circle From 3 Points. F.3 Ellipses. F.3.1. Ellipse Equations. 866 F.3.2 Converting Between Algebraic and Geometric Parameters. 867 F.3.3 Ellipse From 5 Points . Contents G H 871 G.l Mean, Variance, and Covariance. G.l.l Mean . G.l.2 Variance and Covariance. G.1.3 Biased vs. Unbiased Variance. G.2 The Covariance Matrix. G.2.1 Example. G.2.2 Practical Calculation. G.3 Mahalanobis Distance. G.3.1 Definition. G.3.2 Relation to the Euclidean Distance. • · G.3.3 Numerical Considerations. G.3.4 Pre-Mapping Data For Efficient Mahalanobis Matching. G.4 The Gaussian Distribution . G.4.1 Maximum Likelihood Estimation. G.4.2 Gaussian Mixtures. G.4.3 Creating Gaussian Noise. 871 871 871 872 872 873 874 874 874 875
875 876 878 878 880 880 Gaussian Filters. 883 Cascading Gaussian Filters. Gaussian Filters and Scale Space . Effects of Gaussian Filtering in the Frequency Domain. LoG-Approximation by Difference of Gaussians (DoG). 883 883 Writing ImageJ Plugins . 887 ImageJ Plugins. 1.1.1 Program Structure. 1.1.2 A First Example: Inverting an Image. 1.1.3 Plugin My_Inverter_A (PlugInFilter) . 1.1.4 Plugin My_Inverter_B (Plugin). 1.1.5 When To Use Plugin Or PlugInFilter? . . . 1.1.6 Executing ImageJ “Commands”. 1.1.7 ImageJ’s Command Recorder . 887 887 888 888 890 891 892 893 Java Notes . 895 H.4 1.1 J J.l XXIV 869 Statistical Prerequisites. H.l H.2 H.3 I 865 866 866 884 885 Arithmetic. 895 J. 1.1 Integer Division . 895 J. 1.2 Modulus Operator. 896 J.1.3 Mathematical Functions in Class Math. 897 J. 1.4 Numerical Rounding. 898 J. 1.5
Inverse Tangent Function. 899
J.2 J.1.6 Unsigned Byte Data . J.1.7 Classes Float and Double. 900 J.1.8 Testing Floating-Point Values Against Zero . Arrays J.2.1 Creating Arrays. 901 J.2.2 Array Size. 902 J.2.3 Accessing Array Elements. 902 J.2.4 2D Arrays. 903 J.2.5 Arrays of Objects. 905 J.2.6 Searching for Minimum and Maximum Values J.2.7 Sorting Arrays . 899 Contents 901 901 906 906 References. 909 Index. 925 XXV |
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| discipline | Informatik Elektrotechnik / Elektronik / Nachrichtentechnik |
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| spelling | Burger, Wilhelm 1955- Verfasser (DE-588)132219271 aut Digital image processing an algorithmic introduction Wilhelm Burger, Mark J. Burge Third edition Cham, Switzerland Springer [2022] © 2022 XXV, 943 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Texts in computer science Computer science Computational intelligence Image Processing and Computer Vision Signal, Image and Speech Processing Informatik Soft Computing (DE-588)4455833-8 gnd rswk-swf Informatik (DE-588)4026894-9 gnd rswk-swf Bildverarbeitung (DE-588)4006684-8 gnd rswk-swf Java (DE-588)4028527-3 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Bildverarbeitung (DE-588)4006684-8 s Informatik (DE-588)4026894-9 s Soft Computing (DE-588)4455833-8 s DE-604 Java (DE-588)4028527-3 g Burge, Mark James Verfasser (DE-588)132219336 aut Erscheint auch als Online-Ausgabe 978-3-031-05744-1 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=034021843&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=034021843&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Burger, Wilhelm 1955- Burge, Mark James Digital image processing an algorithmic introduction Computer science Computational intelligence Image Processing and Computer Vision Signal, Image and Speech Processing Informatik Soft Computing (DE-588)4455833-8 gnd Informatik (DE-588)4026894-9 gnd Bildverarbeitung (DE-588)4006684-8 gnd |
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| title | Digital image processing an algorithmic introduction |
| title_auth | Digital image processing an algorithmic introduction |
| title_exact_search | Digital image processing an algorithmic introduction |
| title_exact_search_txtP | Digital image processing an algorithmic introduction |
| title_full | Digital image processing an algorithmic introduction Wilhelm Burger, Mark J. Burge |
| title_fullStr | Digital image processing an algorithmic introduction Wilhelm Burger, Mark J. Burge |
| title_full_unstemmed | Digital image processing an algorithmic introduction Wilhelm Burger, Mark J. Burge |
| title_short | Digital image processing |
| title_sort | digital image processing an algorithmic introduction |
| title_sub | an algorithmic introduction |
| topic | Computer science Computational intelligence Image Processing and Computer Vision Signal, Image and Speech Processing Informatik Soft Computing (DE-588)4455833-8 gnd Informatik (DE-588)4026894-9 gnd Bildverarbeitung (DE-588)4006684-8 gnd |
| topic_facet | Computer science Computational intelligence Image Processing and Computer Vision Signal, Image and Speech Processing Informatik Soft Computing Bildverarbeitung Java Lehrbuch |
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