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Lecture-9-h

# Lecture-9-h - Lecture-9 Region Segmentation Segmentation 1...

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Unformatted text preview: Lecture-9 Region Segmentation Segmentation 1 Segmentation • Partition f(x,y) into sub-images: R1, R2, ….,Rn such that the following constraints are satisfied: – n UR i = f ( x, y ) i =1 – Ri I R j = f , i ≠ j – Each sub-mage satisfies a predicate or set of predicates • All pixels in any sub-image musts have the same gray levels. • All pixels in any sub-image must not differ more than some threshold • All pixels in any sub-image may not differ more than some threshold from the mean of the gray of the region • The standard deviation of gray levels in any sub-image must be small. Simple Segmentation Ê 1 if f ( x , y ) < T B ( x, y ) = Á Á 0 Otherwise Ë Ê1 B ( x, y ) = Á Á0 Ë Ê1 B ( x, y ) = Á Á0 Ë if T1 < f ( x, y ) < T2 Otherwise if f ( x , y ) Œ Z Otherwise 2 Histogram Histogram graphs the number of pixels in an image with a Particular gray level as a function of the image of gray levels. For (I=0, I<m, I++) For (J=0, J<m, J++) histogram[f(I,J)]++; Example 3 Segmentation Using Histogram Ê1 B1 ( x, y ) = Á Á0 Ë Ê1 B2 ( x, y ) = Á Á0 Ë Ê1 B3 ( x, y ) = Á Á0 Ë if 0 < f ( x, y ) < T1 Otherwise if T1 < f ( x, y ) < T2 Otherwise if T2 < f ( x, y ) < T3 Otherwise Realistic Histogram 4 Peakiness Test Nˆ Ê (V + Vb ) ˆ Ê Peakiness = Á1 - a ˜.Á1 Á (W .P) ˜ ˜ 2P ¯ Ë Ë ¯ Connected Component È0 Í1 Í Í0 Í Í0 Í0 Î 0 1 0 0 1 0 0 0 1 0 1 1 0 1 1 0˘ 1˙ ˙ 0˙ ˙ 0˙ 0˙ ˚ È0 Íb Í Í0 Í Í0 Í0 Î 0 b 0 0 d 0 0 0 c 0 a a 0 c c 0˘ a˙ ˙ 0˙ ˙ 0˙ 0˙ ˚ 4 5 Connectedness Connected Component È0 Í1 Í Í0 Í Í0 Í0 Î 0 1 0 0 1 0 0 0 1 0 1 1 0 1 1 0˘ 1˙ ˙ 0˙ ˙ 0˙ 0˙ ˚ È0 Íb Í Í0 Í Í0 Í0 Î 0 b 0 0 c 0 0 0 c 0 a a 0 c c 0˘ a˙ ˙ 0˙ ˙ 0˙ 0˙ ˚ 8 6 Recursive Connected Component Algorithm Sequential È0 Í1 Í Í0 Í Í0 Í0 Î 0 1 0 0 1 0 0 0 1 1 1 1 0 1 1 0˘ 1˙ ˙ 0˙ ˙ 0˙ 0˙ ˚ È0 Íb Í Í0 Í Í0 Í0 Î 0 0 a 0˘ b 0 a a˙ ˙ 0 0 0 0˙ ˙ 0 c c 0˙ d c c 0˙ ˚ d=c 7 Sequential Connected Component Algorithm Recursive È0 Í1 Í Í0 Í Í0 Í0 Î 0 1 0 0 1 0 0 0 1 1 1 1 0 1 1 0˘ 1˙ ˙ 0˙ ˙ 0˙ 0˙ ˚ È0 Íb Í Í0 Í Í0 Í0 Î 0 b 0 0 c 0 0 0 c c a a 0 c c 0˘ a˙ ˙ 0˙ ˙ 0˙ 0˙ ˚ 8 Steps in Segmentation Using Histogram 1. Compute the histogram of a given image. 2. Smooth the histogram by averaging peaks and valleys in the histogram. 3. Detect good peaks by applying thresholds at the valleys. 4. Segment the image into several binary images using thresholds at the valleys. 5. Apply connected component algorithm to each binary image find connected regions. Example: Detecting Fingertips 9 Example-II 93 peaks Smoothed Histograms Smoothed histogram (averaging using mask Of size 5) 54 peaks (once) After peakiness 18 Smoothed histogram Smoothed histogram 11 peaks (three times) 21 peaks (twice) After peakiness 4 After peakiness 7 10 Regions (40, 116) (0,40) Regions (116,243) (243,255) 11 ...
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