Digital Image Processing
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1 Digital Image Processing Part 9: Representation and Description AASS Learning Systems Lab, Dep. Teknik Room T1209 (Fr, o'clock) Course Book Chapter
2 Contents 1. Representation and Description 2. Boundary Representation 3. Boundary Descriptors 4. Regional Descriptors 5. Texture Descriptors 6. Global Appearance Descriptors
3 Contents Representation and Description
4 1 Representation and Description Goal description of image information suitable to use for classification, recognition and interpretation decrease the amount of data with as little loss of information as possible Representation Schemes boundary or region-based? external or internal reconstruction? stable under scaling, rotation, and translation? recognition by incomplete or noisy representation?
5 1 Representation and Description Representation and Description based on region boundaries (external characteristics) chain codes, polygonal approximation, signature, Fourier descriptors,... based on regions (internal characteristics) area, P2A, topology, moments, colour distribution,... Descriptors should be discriminative should be stable under variations such as scaling, translation, image plane rotation, out of plane rotation, noise, occlusion, illumination
6 Contents Boundary Representation
7 2 Boundary Representation Representation compact form of the input data that is (more) useful to compute descriptors
8 2 Boundary Representation Chain Codes (Freeman Chain Code) direction of each segment is coded direct application leads to long chain codes that are sensitive to noise to avoid these problems re-sampling using a larger grid spacing is often applied first 4-connected grid 8-connected grid
9 2 Boundary Representation Freeman Chain Code 4-connected grid 8-connected grid
10 2 Boundary Representation Chain Code Issues long chain code + sensitive to noise sub-sample using a coarser grid
11 2 Boundary Representation Chain Code Issues long chain code + sensitive to noise sub-sample using a coarser grid value depends on the starting point treat chain code as circular sequence of direction numbers select cyclic permutation that forms the minimum number not rotation invariant consider the first difference of the chain code (count number of direction changes between consecutive elements of the code) instead of the code itself invariant to 90 /45 rotations
12 2 Boundary Representation Chain Code Issues long chain code + sensitive to noise sub-sample using a coarser grid value depends on the starting point treat chain code as circular sequence of direction numbers select cyclic permutation that forms the minimum number not rotation invariant consider the first difference of the chain code (count number of direction changes between consecutive elements of the code) (counter-clockwise rotation)
13 2 Boundary Representation Chain Code Issues long chain code + sensitive to noise sub-sample using a coarser grid value depends on the starting point treat chain code as circular sequence of direction numbers select cyclic permutation that forms the minimum number not rotation invariant consider the first difference of the chain code normalization to arbitrary rotations align to some dominant feature first
14 2 Boundary Representation Chain Code Issues long chain code + sensitive to noise sub-sample using a coarser grid value depends on the starting point treat chain code as circular sequence of direction numbers select cyclic permutation that forms the minimum number not rotation invariant consider the first difference of the chain code normalization to arbitrary rotations align to some dominant feature first depends on the size of the boundary compensate by altering the size of the re-sampling grid
15 2 Boundary Representation Signatures 2D boundary 1D function distance from centroid as function of angle
16 2 Boundary Representation Signatures (Distance versus Angle) 2D boundary 1D function distance from centroid as function of angle not applicable to all shapes
17 2 Boundary Representation Signatures (Distance versus Angle) 2D boundary 1D function distance from centroid as function of angle invariant to translation not invariant to rotation and scale select a distinct starting point point farthest from the centroid point on the major eigen axis that is farthest from the centroid rescale signature min/max rescaling to values [0,1] (sensitive to noise) divide by the variance of the signature
18 2 Boundary Representation Signatures (Distance versus Angle) 2D boundary 1D function distance from centroid as function of angle invariant to translation not invariant to rotation and scale alternative: angle between the tangent in each point and a reference line histogram slope density function
19 2 Boundary Representation Polygonal Approximations minimum perimeter polygons enclose the boundary by a set of concatenated cells think of the boundary as a rubber band which is allowed to shrink minimum perimeter polygon see GW
20 Contents Boundary Descriptors
21 3 Boundary Descriptors Simple Boundary Descriptors length diameter length of the major axis (connecting the extreme boundary points) basic rectangle major axis x minor axis minor axis perpendicular to the major axis length so that the basic rectangle (= box passing through the intersections of the major and minor axis with the boundary) completely encloses the boundary eccentricity = major axis / minor axis diam ( B) = max i, j [ D( p, p )] i j
22 3 Boundary Descriptors Simple Boundary Descriptors length diameter length of the major axis basic rectangle major axis x minor axis eccentricity = major axis / minor axis Shape Number diam ( B) = max [ D( p, p )] cyclic permutation of the first difference of the chain code that forms the minimum number i, j i j
23 3 Boundary Descriptors Fourier Descriptors represent the boundary as a sequence of coordinates identify the x-axis as the real axis and the y-axis as the imaginary axis sequence of complex vectors calculate discrete Fourier transform (DFT)
24 3 Boundary Descriptors Fourier Descriptors represent the boundary as a sequence of coordinates identify the x-axis as the real axis and the y-axis as the imaginary axis sequence of complex vectors calculate discrete Fourier transform (DFT) boundary can be re-constructed using the inverse DFT approximate reconstruction if only the first P coefficents are used
25 3 Boundary Descriptors Fourier Descriptors
26 Contents Regional Descriptors
27 4 Regional Descriptors Simple Region Descriptors area number of pixels blue = 10 green = 4
28 4 Regional Descriptors Simple Region Descriptors area (number of pixels) P 2 / A (compactness of a region) perimeter = length of boundary unit-less insensitive to uniform scale changes rotation invariant minimal for disc compact not compact
29 4 Regional Descriptors Simple Region Descriptors area (number of pixels) P 2 / A (compactness of a region) unit-less rotation invariant area = 3591, perimeter = 221 P 2 /A=13.60, P 2 /A norm =1.08 minimal for disc normalization P 2 /A norm = (circularity ratio) 2 P 4πA area = 10538, perimeter = 798 P 2 /A=60.43, P 2 /A norm =4.81
30 4 Regional Descriptors Simple Region Descriptors area (number of pixels) P 2 / A (compactness of a region) unit-less rotation invariant minimal for disc normalization P 2 /A norm = 2 P 4πA perfect circle P 2 /A norm = 1 square (side length: a) P 2 /A norm = (4a) 2 / (4πa 2 ) = 4/π 1.27
31 4 Regional Descriptors Simple Region Descriptors area (number of pixels) P 2 / A (compactness of a region) unit-less minimal for disc rotation invariant normalization P 2 / A norm = 2 P 4πA eccentricity = major axis / minor axis longest chord / max perpendicular chord
32 4 Regional Descriptors Simple Region Descriptors area (number of pixels) P 2 / A (compactness) unit-less minimal for disc rotation invariant normalization P 2 / A norm = 2 P 4πA eccentricity = major axis / minor axis longest chord / max perpendicular chord rectangularity area of region / area of bounding rectangle
33 4 Regional Descriptors Topological Descriptors invariant under "rubber sheet" transformations number of connected components C
34 4 Regional Descriptors Topological Descriptors invariant under "rubber sheet" transformations number of connected components C number of holes H
35 4 Regional Descriptors Topological Descriptors invariant under "rubber sheet" transformations number of connected components C number of holes H Euler number E E = C H
36 4 Regional Descriptors Euler Number? Achim Digital Image J. Lilienthal Processing
37 Contents Texture Descriptors
38 5 Texture Descriptors Texture Descriptors no formal definition of texture exists intuitively: measure of smoothness, coarseness, regularity,...
39 5 Texture Descriptors Statistical Descriptors statistical moments of the grey-level histogram z: random variable for intensity p(z): corresponding histogram L: number of distinct intensity levels compute n th moments m: mean intensity µ L 1 n ( z) ( z m) p( z ) = n i i i= 0 L 1 i= 0 ( ) m= zp i z i
40 5 Texture Descriptors Statistical Descriptors statistical moments of the grey-level histogram z: random variable for intensity p(z): corresponding histogram L: number of distinct intensity levels compute n th moments m: mean intensity µ 0 = 1, µ 1 = 0 µ 2 = σ 2 (z) (variance) µ 3 (measure of skewness) µ 4 (measure of relative flatness),... µ L 1 n ( z) ( z m) p( z ) = n i i i= 0 L 1 i= 0 ( ) m= zp i z i
41 5 Texture Descriptors Statistical Descriptors σ : measure of average contrast
42 5 Texture Descriptors Statistical Descriptors relative smoothness R = σ ( z) 0 for areas of constant intensity 1 for large values of σ 2 1
43 5 Texture Descriptors Statistical Descriptors relative smoothness 0 for areas of constant intensity measure of uniformity lowest if uniform highest if p(z i ) = 1 and p(z j ) = 0 for j i 1 1+σ R = 1 2 ( z) L 1 2 U( z) = p zi i= 0 ( )
44 5 Texture Descriptors Statistical Descriptors relative smoothness 0 for areas of constant intensity measure of uniformity lowest if uniform average entropy measure of variablility / randomness 0 for p(z i ) = 1 and p(z j ) = 0 for j i positiv otherwise (max. for uniform distribution) L 1 i= σ R = 1 2 ( z) L 1 2 U( z) = p zi i= 0 ( ) ( ) ( ) e( z) p z log p z = i 2 i
45 5 Texture Descriptors Statistical Descriptors
46 5 Texture Descriptors Statistical Descriptors co-occurrence matrix consider also relative positions of pixels for statistical description define position operator P for example: "one pixel to the right and one pixel below" count co-occurring intensity levels i and j in matrix g ij image
47 5 Texture Descriptors Statistical Descriptors co-occurrence matrix consider also relative positions of pixels for statistical description define position operator P for example: "one pixel to the right and one pixel below" count co-occurring intensity levels i and j in matrix g ij image
48 5 Texture Descriptors Statistical Descriptors co-occurrence matrix consider also relative positions of pixels for statistical description define position operator P for example: "one pixel to the right and one pixel below" count co-occurring intensity levels i and j in matrix g ij image
49 5 Texture Descriptors Statistical Descriptors co-occurrence matrix consider also relative positions of pixels for statistical description define position operator P for example: "one pixel to the right and one pixel below" count co-occurring intensity levels i and j in matrix g ij image
50 5 Texture Descriptors Statistical Descriptors co-occurrence matrix consider also relative positions of pixels for statistical description define position operator P for example: "one pixel to the right and one pixel below" count co-occurring intensity levels i and j in matrix g ij image
51 5 Texture Descriptors Statistical Descriptors co-occurrence matrix consider also relative positions of pixels for statistical description define position operator P for example: "one pixel to the right and one pixel below" count co-occurring intensity levels i and j in matrix g ij image
52 5 Texture Descriptors Statistical Descriptors co-occurrence matrix consider also relative positions of pixels for statistical description define position operator P for example: "one pixel to the right and one pixel below" count co-occurring intensity levels i and j in matrix g ij normalize co-occurrence numbers g ij p ij consider statistical measures over p ij max (p ij ) correlation (how strong are values correlated given P) contrast (measure of contrast given P)...
53 Contents Global Appearance Descriptors
54 6 Global Descriptors Global Descriptors objects / scenes represented by a set of views no 3D model needed! Swain/Ballard 1991
55 6 Global Descriptors Global Descriptors objects / scenes represented by a set of views each view represented by a descriptor =
56 6 Global Descriptors Global Descriptors variations translation scale image plane rotations out of plane rotation noise occlusion illumination
57 6 Global Descriptors Global Descriptors variations translation scale image plane rotations out of plane rotation noise occlusion illumination
58 6 Global Descriptors Global Descriptors variations translation scale image plane rotations out of plane rotation noise occlusion illumination some modes of variation built in the descriptor
59 6 Global Descriptors Global Descriptors variations translation scale image plane rotations out of plane rotation noise occlusion illumination some modes of variation built in the descriptor some modes incorporated in the training data
60 6 Global Descriptors Greylevel/Color Histograms no spatial information largely invariant to translation scale image plane rotations out of plane rotation noise occlusion illumination
61 6 Global Descriptors Color Histograms, RGB Swain/Ballard 1991
62 6 Global Descriptors Color Histograms, RGB rg normalize to intensity I = R + G + B "chromatic representation" less affected by illumination changes only two parameters (r + g + b = 1)
63 6 Global Descriptors Color Histograms, Build Object Database store descriptors and their labels Swain/Ballard 1991
64 6 Global Descriptors Color Histograms, Recognize Objects store descriptors and their labels query unknown object compute descriptor compare to database descriptors etc. Swain/Ballard 1991
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