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Unformatted text preview: Image Segmentation
Part 2 Thresholding and Regionbased Segmentation Introduction The simplest property that pixels in a region can share is intensity. So, a natural way to segment such regions is through thresholding, the separation of light and dark regions. Thresholding is the simplest form of segmentation Useful for scenes containing solid objects resting upon a contrasting background but with uniform gray levels. Introduction Thresholding creates binary images from grey-level ones by turning all pixels below some value to zero and all pixels about that value to one. The pivotal value that is used to decide whether any given pixel is to be black or white is the threshold. What you want to do with pixels at the threshold doesn't matter, as long as you're consistent. Thresholding Foundation: Thresholding In Figure (a): light objects in dark background To extract the objects: Select a T that separates the objects from the background i.e. any (x,y) for which f(x,y)>T is an object point. Thresholding In Figure (b): a more general case of this approach (multilevel thresholding) So: (x,y) belongs: To one object class if T1<f(x,y)T2 To the other if f(x,y)>T2 To the background if f(x,y)T1 Thresholding If g(x, y) is a thresholded version of f(x, y) at some global threshold T, A thresholded image (with a single threshold):
1 if g ( x, y ) = 0 if f ( x, y ) > T f ( x, y ) T
(objects) (background) Thresholding Thresholding can be viewed as an operation that involves tests against a function T of the form: T = T [ x, y, p ( x, y ), f ( x, y )]
f(x,y) is the gray level of point (x,y) p(x,y) denotes some local property of this point, e.g. the average level of a neighborhood centered on (x,y) Thresholding When T depends only on f(x,y) global threshold When T depends on both f(x,y) and p(x,y) local threshold When in addition, T depends on x and y adaptive threshold Thresholding algorithm Search all the pixels f(i,j) of the image f. An image element g(i,j) of the segmented image is an object pixel if f(i,j) >=T, and is a background pixel otherwise. Note that.. Correct threshold selection is crucial for successful threshold segmentation. Threshold selection can be interactive or can be the result of some threshold detection Threshold Selection Success of thresholding depends on the threshold (T) chosen. How do we select the best threshold??? Threshold detection methods One method of doing this is to always threshold the image at 128, the midpoint in the histogram. This is not an intelligent approach though, since it doesn't account for the frequencies within the image. Threshold mid value Below is another picture of a B-2, this time demonstrating that despite there being a strong constrast between the foreground and background, picking 128 as the threshold point yields very poor results: An iterative approach can be used. 1. Algorithm:
Pick an initial threshold value, t (say 128). Calculate the mean values in the histogram below (m1) and above (m2) the threshold t. Calculate new threshold. tnew = (m1 + m2) / 2. If the threshold has stabilized (t = tnew), this is your threshold level. Otherwise, t become tnew and reiterate from step 2. 2. 3. 4. Threshold via Iterative Approach When run on our B-2 image, it settles at 74 as the optimum threshold. This produces the following image: Basic Global Thresholding Global thresholding. The value of the thresholding gray level is held constant throughout the image. Fixed global threshold work well if the background gray level is reasonably constant throughout, and if the objects all have approximately equal constrast above the background Basic Global Thresholding To partition the image histogram by using a single threshold T. Then the image is scanned and labels are assigned. This technique is successful in highly controlled environments. Adaptive Thresholding Using variable threshold values Threshold value varies over the image as a function of local image characteristic. Adaptive Thresholding
1. Image f is divided into subimages fc. A threshold is determined independently in each subimage If a threshold cannot be determined in some subimage, it can be interpolated from thresholds determined in neighboring subimages. Each subimage is then processed with respect to its local threshold. 2. 3. 4. Region-based Segmentation Edge-based segmentation: borders between regions Region-based segmentation: direct construction of regions Region growing techniques are generally better in noisy images where edges are extremely difficult to detect Region-Oriented Segmentation Segmentation is a process that partitions R into n subregions R1, R2, ..., Rn such that:
a) n Ri = R i =1 b) Ri is a connected region, i = 1, 2, ..., n c) Ri Rj = 0 for all i and j, ij e) P(Ri Rj) = FALSE for ij P(R d) P(Ri) = TRUE for i = 1, 2, ..., n i): logical predicate Interpretation of the conditions a) indicates that the segmentation must be complete i.e. every pixel must be in the region. b) requires that points in a region must be connected in some predefined connectivity sense. c) indicates that the region must be disjoint. d) deals with the properties that must be satisfied by the pixels in a segmented region (e.g. gray level). e) indicates that region R1 and R2 are different in certain sense. Segmentation Criterion Homogeneity of regions is used as the main segmentation criterion in region growing The criteria for homogeneity: gray level color, texture shape model etc. Region Growing by Pixel Aggregation Is a procedure that groups pixels or subregions into larger regions based on predefined criteria. The approach starts with a set of "seed" points and from these grow regions by appending to each seed point those neighboring pixels that have similar properties. Region Growing by Pixel Aggregation The selection of seeds depends on: Type of problem under consideration Type of image data available. For example, the analysis of land-use satellite imagery depends heavily on the use of color. When the images are monochrome, region analysis must be carried out with a set of descriptors based on gray levels and spatial properties Region Growing Region Merging Start at small segment (e.g. one pixel) that satisfying homogeneity criterion Merge adjacent regions that satisfy merging criterion If no regions can be merged stop Region Splitting Start with whole image Split region if not homogeneous Stop if no region can be split anymore Region Split and Merge Subdivide an image initially into a set of arbitrary, disjointed regions and then merge and/or split the regions in an attempt to satisfy the conditions of region-oriented segmentation. Quadtree-based algorithm Split-and-Merge Algorithm Data Structure is Pyramid/Quadtree If region is not homogeneous split (4 children) If all 4 regions with same parent can be merged, then merge. If no split or merge is possible, merge any two adjacent regions that are homogeneous (even on different pyramid levels) Region-based Segmentation ...
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- Winter '09