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Image Understanding 2

Image Understanding 2. Outline: Guzman Scene Analysis Local and Global Consistency Edge Detection Laplacians and Zero Crossings Segmentation into Regions Image Connected Components Gestalt Grouping Morphology. Image Understanding 2. Outline: Guzman Scene Analysis

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Image Understanding 2

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  1. Image Understanding 2 Outline: Guzman Scene Analysis Local and Global Consistency Edge Detection Laplacians and Zero Crossings Segmentation into Regions Image Connected Components Gestalt Grouping Morphology CSE 415 -- (c) S. Tanimoto, 2008 Image Understanding II

  2. Image Understanding 2 Outline: Guzman Scene Analysis Local and Global Consistency Edge Detection Laplacians and Zero Crossings Segmentation into Regions Image Connected Components Gestalt Grouping Morphology CSE 415 -- (c) S. Tanimoto, 2008 Image Understanding II

  3. Blocks-World Scene Analysis(Adolfo Guzman, MIT AI Lab, 1967) • Input: a line drawing representing a 3D scene consisting of polyhedra • Output: lists of faces grouped into objects • Method: (a) classify vertices, (b) link faces according to rules, (c) extract connected components of doubly linked regions. CSE 415 -- (c) S. Tanimoto, 2008 Image Understanding II

  4. CSE 415 -- (c) S. Tanimoto, 2008 Image Understanding II

  5. Guzman Vertex Categories ell, arrow, fork, tee, kay CSE 415 -- (c) S. Tanimoto, 2008 Image Understanding II

  6. Guzman Linking Rules ell, arrow, fork, tee, kay CSE 415 -- (c) S. Tanimoto, 2008 Image Understanding II

  7. Guzman Face Grouping Criterion:Two adjacent faces must be doubly linked to be considered part of the same object. Obj1: (A B C) Obj2: (D E F G) A C B E D G F CSE 415 -- (c) S. Tanimoto, 2008 Image Understanding II

  8. Image Understanding 2 Outline: Guzman Scene Analysis Local and Global Consistency Edge Detection Laplacians and Zero Crossings Segmentation into Regions Image Connected Components Gestalt Grouping Morphology CSE 415 -- (c) S. Tanimoto, 2008 Image Understanding II

  9. Impossible Figures Locally consistent, globally inconsistent CSE 415 -- (c) S. Tanimoto, 2008 Image Understanding II

  10. Image Understanding 2 Outline: Guzman Scene Analysis Local and Global Consistency Edge Detection Laplacians and Zero Crossings Segmentation into Regions Image Connected Components Gestalt Grouping Morphology CSE 415 -- (c) S. Tanimoto, 2008 Image Understanding II

  11. Edge Detection Why? Find boundaries of objects in order to compute their features: shape, area, moments, corner locations, etc. Methods: Compute measures of change in the neighborhood of each pixel. Trace boundaries Transform each neighborhood into a vector space whose basis includes "edge" vectors. CSE 415 -- (c) S. Tanimoto, 2008 Image Understanding II

  12. Local Edge Detectors Horizontal differences: a – b Both horiz. & vertical diffs. Roberts' cross operator (a-d)2 +(b-c)2 a b a b c d CSE 415 -- (c) S. Tanimoto, 2008 Image Understanding II

  13. Frei-Chen Edge Detection Express each 3x3 neighborhood as a vector. N = <a, b, c, d, e, f, g, h> a b a c d e f g h CSE 415 -- (c) S. Tanimoto, 2008 Image Understanding II

  14. Frei-Chen Edge Det. (cont) Transform it linearly into the 9D vector space spanned by the following basis vectors (each shown in 3x3 format) CSE 415 -- (c) S. Tanimoto, 2008 Image Understanding II

  15. Image Understanding 2 Outline: Guzman Scene Analysis Local and Global Consistency Edge Detection Laplacians and Zero Crossings Segmentation into Regions Image Connected Components Gestalt Grouping Morphology CSE 415 -- (c) S. Tanimoto, 2008 Image Understanding II

  16. Edge Finding with the Laplacian Instead of using 1st derivatives, let's consider 2nd derivatives. The Laplacian effectively finds subtle changes in intensity. 2 f(x,y) = 2 f(x,y)/x2 + 2f(x,y)/y2 discrete approximation: 0 -1 0 -1 4 -1 0 -1 0 CSE 415 -- (c) S. Tanimoto, 2008 Image Understanding II

  17. Laplacian: Very Sensitive to Noise Remedy: First, smooth the signal with a Gaussian filter. g(x,y) = 1/(22) exp(-(x2+y2)/22 ) Then take the Laplacian. Or, directly convolve directly with a Laplacian of Gaussian (LOG). CSE 415 -- (c) S. Tanimoto, 2008 Image Understanding II

  18. Zero Crossings The edges tend to be where the second derivative crosses 0. CSE 415 -- (c) S. Tanimoto, 2008 Image Understanding II

  19. Zero Crossings: Example (a) orig. (b) LoG with  = 1, (c) zero crossings. R Fischer et al. http://homepages.inf.ed.ac.uk/rbf/HIPR2/zeros.htm CSE 415 -- (c) S. Tanimoto, 2008 Image Understanding II

  20. Image Understanding 2 Outline: Guzman Scene Analysis Local and Global Consistency Edge Detection Laplacians and Zero Crossings Segmentation into Regions Image Connected Components Gestalt Grouping Morphology CSE 415 -- (c) S. Tanimoto, 2008 Image Understanding II

  21. 4- and 8-adjacency If two neighboring pixels share a side, they are 4-adjacent. d's 4-adjacent neighbors are: b, c, e, g If two neighboring pixels share a corner, they are 8-adjacent d's 8-adjacent neighbors are: a,b,c,e,f,g,h a b a c d e f g h CSE 415 -- (c) S. Tanimoto, 2008 Image Understanding II

  22. 4- and 8-connectedness A set of pixels R is said to be 4-connected, provided for any pi, pj in R, there is a chain [(pi, pi' ), (pi' , pi'' ), ..., (pk, pj)] involving only pixels in R, and each pair in the chain is 4-adjacent. The chain may be of length 0. R is 8-connected, iff there exists such a chain where each pair is 8-adjacent. CSE 415 -- (c) S. Tanimoto, 2008 Image Understanding II

  23. 4- and 8-connected components 4-connected components of black: 4 8-connected components of black: 2 4-connected components of white: 2 8-connected components of white: 2 CSE 415 -- (c) S. Tanimoto, 2008 Image Understanding II

  24. Segmentation into Regions "Dual approach" to edge detection. Let P be a digital image: P = {p0, p1, ..., pn-1} A segmentation S = {R0, R1, ..., Rm-1} is a partition of P, such that For each i, Ri is 4-connected, and Ri is "uniform", and for all i,j if Ri is adjacent to Rj, then (Ri U Rj) is not uniform. CSE 415 -- (c) S. Tanimoto, 2008 Image Understanding II

  25. Image Understanding 2 Outline: Guzman Scene Analysis Local and Global Consistency Edge Detection Laplacians and Zero Crossings Segmentation into Regions Image Connected Components Gestalt Grouping Morphology CSE 415 -- (c) S. Tanimoto, 2008 Image Understanding II

  26. Image Connected Components Can compute a segmentation if U(R) means all pixels in R have the same pixel value (e.g., intensity, color, etc.) Algorithm: Initialize a UNION-FIND ADT instance, with each pixel in its own subset. Scan the image. At each pixel p, check its neighbor r to the right. p and r have the same pixel value, determine whether FIND(p) = FIND(r), and if not, perform UNION(FIND(p), FIND(r)). Then check the pixel q below doing the same tests and possible UNION. When the scan is complete, each subset represents one 4-connected component of the image. CSE 415 -- (c) S. Tanimoto, 2008 Image Understanding II

  27. Image Understanding 2 Outline: Guzman Scene Analysis Local and Global Consistency Edge Detection Laplacians and Zero Crossings Segmentation into Regions Image Connected Components Gestalt Grouping Morphology CSE 415 -- (c) S. Tanimoto, 2008 Image Understanding II

  28. Gestalt Grouping Identification of regions using a uniformity predicate based on wider-neighborhood features (e.g., texture). CSE 415 -- (c) S. Tanimoto, 2008 Image Understanding II

  29. Gestalt Grouping CSE 415 -- (c) S. Tanimoto, 2008 Image Understanding II

  30. Gestalt Grouping Texture element = “texel” Texel directionality Texel granularity Alignments of endpoints Spacing of texels Groups cue for surfaces, objects. CSE 415 -- (c) S. Tanimoto, 2008 Image Understanding II

  31. Image Understanding 2 Outline: Guzman Scene Analysis Local and Global Consistency Edge Detection Laplacians and Zero Crossings Segmentation into Regions Image Connected Components Gestalt Grouping Morphology CSE 415 -- (c) S. Tanimoto, 2008 Image Understanding II

  32. "Mathematical Morphology" Developed at the Ecoles des Mines, France by J. Serra, from mathematical ideas of Minkowski. Idea is to take two sets of points in space and obtain a new set. Set A: the main set. Set B: the "structuring element" Set C: the result. CSE 415 -- (c) S. Tanimoto, 2008 Image Understanding II

  33. Math. Morph. Operation 1: "Erosion" Consider each point b of B to be a vector and use it to translate a copy of A getting Ab Take the intersection of all the Ab The result is called the erosion of A by B. CSE 415 -- (c) S. Tanimoto, 2008 Image Understanding II

  34. Erosion: example A: 0 1 1 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 0 0 B: 1 1 C: 0 0 1 0 0 0 1 1 0 0 0 0 1 1 0 0 0 0 0 0 CSE 415 -- (c) S. Tanimoto, 2008 Image Understanding II

  35. Dilation: Take Union instead of Intersection. A: 0 1 1 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 0 0 B: 1 1 C: 0 1 1 1 0 1 1 1 1 0 0 1 1 1 1 0 0 1 1 0 CSE 415 -- (c) S. Tanimoto, 2008 Image Understanding II

  36. Opening: Erode by B, then Dilate by –B (B rotated by ) A: 0 1 1 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 0 0 B: 1 1 C: 0 1 1 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 0 CSE 415 -- (c) S. Tanimoto, 2008 Image Understanding II

  37. Closing: Dilate by B, then Erode by –B (B rotated by ) A: 0 1 1 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 0 0 B: 1 1 C: 0 1 1 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 0 0 (In this example, erosion undoes the dilation.) CSE 415 -- (c) S. Tanimoto, 2008 Image Understanding II

  38. Closing – another example A: 0 1 1 0 0 1 0 1 0 0 0 1 0 1 0 0 0 1 0 0 B: 1 1 C: 0 1 1 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 0 0 (In this example, closing fills in holes.) CSE 415 -- (c) S. Tanimoto, 2008 Image Understanding II

  39. Math. Morphol. Uses Repair regions corrupted by noise; Eliminate small regions Identify holes, bays, protrusions, isthmi, peninsulas, and specific shapes such as crosses. Printed circuit board inspection (find cracks, spurious wires.) Popular primitives for writing industrial machine vision apps. CSE 415 -- (c) S. Tanimoto, 2008 Image Understanding II

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