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Image representation

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Image representation

1. 1. 1 Image Representation
2. 2. Introduction • After an image is segmented into regions; the resulting aggregate of segmented pixels is represented & described for further computer processing. • Representing a region involves two choices:  in terms of its external characteristics (boundary)  in terms of its internal characteristics (pixels comprising the region) • Above scheme is only part of task of making data useful to computer. • Next task is to Describe the region based on representation. • Ex. A region may be represented by its boundary & its boundary is described by features such as its length, the orientation of straight line joining its extreme points & number of concavities in the boundary. 2
3. 3. Introduction Q. Which to choose when? • External representation is chosen when primary focus is on shape characteristics. • Internal representation is chosen when primary focus is on regional properties such as color & texture. • Sometimes it is necessary to choose both representations. 3
4. 4. Representation • It deals with compaction of segmented data into representations that facilitate the computation of descriptors. 1) Boundary (Border) Following: Most of the algorithms require that points in the boundary of a region be ordered in a clockwise (or counterclockwise) direction. We assume i) we work with binary images with object and background represented as 1 & 0 respectively. ii) Images are padded with borders of 0s to eliminate the possibility of object merging with image border. 4
5. 5. Representation 1) Let the starting point b0 be the uppermost, leftmost point in the image. c0 the west neighbor of b0. Examine 8 neighbors of b0 starting at c0 & proceed in clockwise direction. 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Let b1 denote first neighbor encountered with value 1 & c1 be background point immediately preceding b1 in the sequence. 5
6. 6. Representation 2) Let b = b1 & c = c1 3) Let the 8-neighbors of b, starting at c & proceeding in clockwise directions be denoted by n1, n2, …..n8. Find first nk labeled 1. 4) Let b = nk & c = nk-1 c c0 b0 1 1 1 b 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 6
7. 7. Representation 2) Let b = b1 & c = c1 3) Let the 8-neighbors of b, starting at c & proceeding in clockwise directions be denoted by n1, n2, …..n8. Find first nk labeled 1. 4) Let b = nk & c = nk-1 c b0 1 b 1 b 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 7
8. 8. Representation 5) Repeat step 3 & 4 until b = b0 & next boundary point found is b1. The sequence of b points found when the algorithm stops constitutes the set of ordered boundary points. The algorithm is also called as Moore boundary Tracking algorithm.
9. 9. Representation 2) Chain codes: They are used to represent a boundary by a connected sequence of straight line segments of specified length & direction. Typically this representation is based on 4- or 8-connectivity of segments. The direction of each segment is coded by using a numbering scheme. 1 3 2 1 2 0 4 0 3 5 6 7 9
10. 10. Representation • A boundary code formed as a sequence of such directional numbers is referred to as a Freeman chain code. • Digital images are acquired & processed in a grid format with equal spacing in x and y directions. • So a chain code can be generated by following a boundary (say clockwise direction) and assigning a direction to the segments connecting every pair of pixels. Unacceptable method: (because) 1) Resulting chain tends to be quite long 2) Any small disturbances along the boundary due to noise or imperfect segmentation can cause changes in code. 10
11. 11. Representation 11 0033333323221211101101 076666553321212
12. 12. Representation • A solution to this problem is to resample the boundary by selecting a larger grid spacing. • Then, as the boundary is traversed, a boundary point is assigned to each node of the large grid, depending upon the proximity of original boundary to that node. • The re-sampled boundary can now be represented by a 4- or 8-code. • The accuracy of the resulting code representation depends on the spacing of the sampling grid. 12
13. 13. Representation 3) Polygon Approximation using Min. Perimeter Polygons: • A digital boundary can be approximated with arbitrary accuracy by a polygon. • For a closed boundary, approx becomes exact when no. of segments of polygon = no. of points in the boundary. • Goal of poly. Approx is to capture the essence of the shape in a given boundary using fewest no. of segments. • Min. Perimeter Polygon (MPP): – An approach for generating an algorithm to compute MPPs is to enclose a boundary by a set of concatenated cells. – Think boundary as a r u b b e r b a n d . – As allowed to shrink, it will be constrained by the inner & outer walls of the bounding regions. 13
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15. 15. Representation • This shrinking produces the shape of a polygon of min. perimeter. • Size of cells determine the accuracy of the polygonal approximation. • In the limit if size of each cell corresponds to a pixel in the boundary , the error in each cell between the boundary & the MPP approx. at most would be √2d, where d-min possible pixel distance. 15
16. 16. Representation • The objective is to use the largest possible cell size acceptable in a given application. • Thus, producing MPPs with fewest no. of vertices. • The cellular approach reduces the shape of the object enclosed by the original boundary to the area circumscribed by the gray wall. • Fig. shows shape in dark gray. • Its boundary consists of 4-connected straight line segments. 16
17. 17. Representation • If we traverse the boundary in counter clockwise direction. • Every turn encountered in the transversal will be either a convex (white) or concave(black) vertex, with the angle of vertex being an interior angle of the 4-connected boundary. • Every concave vertex has a corresponding mirror vertex in light gray wall, located diagonally opposite. • MPP vertices coincide with the convex vertices of inner wall and mirror concave vertices of outer wall. 17
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19. 19. 19 Thank You