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E.G.M. PetrakisImage Segmentation1 Segmentation is the process of partitioning an image into regions –region: group of connected pixels with similar properties –properties: gray levels, colors, textures, motion characteristics (motion vectors), edge continuity … There are two approaches to segmentation –region segmentation –edge segmentation

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E.G.M. PetrakisImage Segmentation2 Edges and Regions In ideal images, a region is bounded by a closed contour –the close contours may be obtained from the regions by edge detection –the regions may be obtained from the closed contours by boundary-filling In real images, it is rare to obtain regions from contours directly and vice versa

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E.G.M. PetrakisImage Segmentation3 Regions and Objects Regions are important for the interpretation of images because they may correspond to objects in a scene An image may contain several objects and each object may contain several regions corresponding to different parts of an object Due to a number of factors (noise, bad illumination, 3D world etc.) segmentation is usually not perfect Image Interpretation requires object specific knowledge

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E.G.M. PetrakisImage Segmentation4 Image with many objects Each object consists of several regions

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E.G.M. PetrakisImage Segmentation5 Region Segmentation Region Segmentation: the pixels of the same object are grouped together and are marked to indicate that they form a region Criteria for region segmentation: pixels may be assigned to the same region if they have similar intensity values and they are close to one another

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E.G.M. PetrakisImage Segmentation6 Edge Segmentation Find all pixels on region boundaries Canny Operator –apply Gaussian smoothing –apply edge detection –remove false edges (e.g., noise) –thin the edge boundary is 1 pixel wide –fill the gaps recover missing edges –put boundary pixels in order all pixels in a list Ideally closed boundaries

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E.G.M. PetrakisImage Segmentation7 Edge Following There may exist gaps and noisy edges in the output of Canny Fill gaps and follow the edge in many directions –there may exist more than one regions meeting each other –not all directions are promising continuity proximity intensity length direction

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E.G.M. PetrakisImage Segmentation8 Edge Following as a Graph Traversal Problem

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E.G.M. PetrakisImage Segmentation9 Graph Traversal Edge following on a graph can be viewed as a minimization (or maximization) problem –the most promising path is the one which maximizes a function Φ(i,j) –promising paths correspond to strong edges Graph search can be hard combinatorial Can become very slow –Dynamic Programming (DP) –Heuristics

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E.G.M. PetrakisImage Segmentation10 Criterion Φ(C) The edge C with maximum Φ is the most promising –Φ(C) = Σφ(i,j) over all points on a curve –Σφ(i,j) = average{intensity} - average{angle} –takes averages over all points on a path In places where the curve splits into 2 or more directions (paths), follow the direction with the maximum φ –this situation changes after a while and may be necessary to backtrack to an earlier point

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E.G.M. PetrakisImage Segmentation11 555 555 7474 3536 1617 1616 66 second path promising at 7 φ=17/3-0 φ=14/3-π/(4 * 3) edges directions φ=22/6-0 first path φ=33/6- 2 * π/(4 * 6) promising at 6

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E.G.M. PetrakisImage Segmentation12 Using the maximum cost Φ criterion to find the cell boundaries in microscope images a.a stage in the search process b.the completed boundary

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E.G.M. PetrakisImage Segmentation13 Region Segmentation Analyze the grey value distribution (histogram) of the image –assumption: objects are dark against a light background –their grey-value distributions can be separated putting thresholds between them –convert a grey-level image into a binary one by applying carefully selected thresholds

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E.G.M. PetrakisImage Segmentation14 Many Regions One threshold two regions –black pixels: object –white pixels: background More than two thresholds more than two regions with different intensity values

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E.G.M. PetrakisImage Segmentation15 (1) Peakiness Detection Algorithm 1.Find the two highest local maxima g i, g j in the histogram that are at least at distance d apart d is user defined 2.Find the lowest point g k in the histogram between g i and g j 3.Peakiness = min{H(g i ),H(g j )}/H(g k ) 4.Take the combination (g i,g j,g k ) with the highest peakiness 5.Threshold the image at T=g k 6.N thresholds: take the N greater peakinesses (T i =g ki )

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E.G.M. PetrakisImage Segmentation16 (2) Iterative Algorithm 1.Compute a threshold T T: mean gray value of image 2.Partition the image into R 1, R 2 using T 3.Compute the mean values μ 1,μ 2 of R 1,R 2 4.Select a new threshold T=1/2(μ 1 +μ 2 ) 5.Repeat steps 2-4 until μ 1, μ 2 do not change

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E.G.M. PetrakisImage Segmentation17 (3) Adaptive Thresholding The same threshold is not usable everywhere in the image e.g., uneven illumination 1.Partition the image into m x m subimages 2.Select a threshold T ij for each subimage apply 1 st or 2 nd threshold selection algorithm 3.Compute the union of the thresholded subimages

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E.G.M. PetrakisImage Segmentation18 a.original image with uniform illumination b.histogram of a c.simulated uneven illumination d.image a with uneven illumination added e.histogram of image d f.thresholding at T=72 failed!!

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E.G.M. PetrakisImage Segmentation19 (4) Double Thresholding 1.Select threshold T 1 (apply 1 st or 2 nd algorithm) 2.Set T 2 = T 1 + ε (ε is user defined) 3.Compute regions R 1, R 2, R 3 : a.R 1 : pixels with gray values less than T 1 b.R 2 : pixels with gray values between T 1 and T 2 c.R 3 : pixels with gray values above T 2 4.Visit each pixel of R 2 : if the pixel has a neighbor in R 1, reassign it to R 1 5.Repeat step 4 until no pixels of R 2 are reassigned 6.Reassign all pixels remaining in R 2 to R 3

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Thresholding Thresholding is usually the first step in any segmentation approach We have talked about simple single value thresholding already Single value.

Thresholding Thresholding is usually the first step in any segmentation approach We have talked about simple single value thresholding already Single value.

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