Graph Based Image Segmentation

Transcription

1 Graph Based Image Segmentation Sandeep Chalasani Department of Electrical & Computer Engineering Clemson University Abstract Segmentation of images into regions for measurement or recognition is probably the most single problem area for image analysis due to the reason that it is subjective and computation is costly. Graph based imagesegmentation is a fast and efficient method of generating a set of segments from an image. They super cede old edge-based approaches as they not only consider local pixel-based features, but also look at global similarities within the image. This paper presents graph based image segmentation algorithm that captures certain perceptually important non-local image characteristics and is also computationally efficient. 1. Introduction Perceptual grouping makes a very important role in human visual perception as emphasized by the Gestalt school of psychologists. The Gestalt theory identified a set of laws of grouping under ideal simplistic settings for artificial stimuli: elements are structured into groups sharing a common feature, e.g. intensity, color, or motion. There are many implementations of image segmentation. These algorithms are basically categorized into three groups: 1) clustering the low level feature, such as histogram thresholding and k-means, 2) edge linking such as dynamic programming, relaxation approach, and saliency network, and 3) region operation, such as region growing, region splitting and merging. A wide range of computational vision problems could make good use of segmented images, were such segmentations reliably and efficiently computable. 2. Graph Based Segmentation The graph based image segmentation is based on selecting edges from a graph, where each pixel corresponds to a node in the graph. Weights on each edge measure the dissimilarity between pixels. The segmentation algorithm defines the boundaries between regions by comparing two quantities Intensity differences across the boundary and Intensity difference between neighboring pixels within each region. This is useful knowing that the intensity differences across the boundary are important if they are large relative to the intensity differences inside at least one of the regions. This results in a method that obeys certain non-obvious global properties. Let the internal difference of a component C in an image be Int (C) = max w(e) Where w(e) in the largest weight in the Minimum Spanning Tree of the component. Let the difference between two components C1, C2 to be the minimum weight edge connecting the two components. That is, Dif(C1,C2) = min w((v i,v j )) The boundary between a pair or components is determined by checking if the difference between the components, Dif (C1, C2), is large relative to the internal difference within at least one of the components, Int (C1) and Int (C2). A threshold function is used to determine the degree to which the difference between

2 components must be larger than minimum internal difference, i.e., D (C1, C2) true if Dif C1, C2 > MInt(C1, C2) = false otherwise Where the minimum internal difference MInt is defined by MInt(C1,C2)=min(Int(C1)+τ(C1);Int(C2)+τ(C2)) partition the image into regions. A disjoint set can be made to perform the following operations: MAKE-SET(x): create a new set with only x, assuming x is not already in some other set. UNION(x, y): combine the two sets containing x and y into one new set. A new representative is selected. FIND-SET(x): return the representative of the set containing x. 3.1 Algorithm 2.1 Algorithm 1. The input is a graph G = (V, E), where V are the n vertices and E are m edges. Each edge has a corresponding weight, which is a measure of dissimilarity between adjacent pixels. 2. Perform the segmentation such that teach component C ϵ S corresponds to a connected component in a graph G = (V; E ), where E ϵ E. 3. If the weight of the edge connecting two vertices in adjacent components is small compared to the internal difference of both the components, then merge the two components, otherwise do nothing. 4. Repeat Step 3for q = 1, 2,..., m. 5. Return S m the components after the final iteration function MakeSet(x) x.parent := x x.rank := 0 function Union(x, y) xroot := Find(x) yroot := Find(y) if xroot.rank > yroot.rank yroot.parent := xroot else if xroot.rank < yroot.rank xroot.parent := yroot else if xroot!= yroot yroot.parent := xroot xroot.rank := xroot.rank + 1 function Find(x) if x.parent == x return x else x.parent := Find(x.parent) return x.parent 3. Disjoint Set Data Structure A disjoint-set is a collection of sets S = {S 1, S 2,, S k } of distinct dynamic sets which is used to keep track of segments of a broken element. Each set is identified by a member of the set, called representative. In the implementation of this algorithm we make use of disjoint sets to

3 4. Results Figure 1: Original Image. Figure 2: Segmentation results produced by the algorithm (τ = 150,min_val = 1000).

4 Figure 3: Segmentation results produced by the algorithm (τ = 150,min_val = 500). Figure 4: Segmentation results produced by the algorithm (τ = 150,min_val = 750).

5 Image: holes.pgm Figure 5: Original Image Figure 8: Segmentation results produced by the algorithm (τ = 150,min_val = 150). 5. Conclusions Figure 6: Segmentation results produced by the algorithm (τ = 150,min_val = 250). Image: cells_small.pgm Figure 7: Original Image The Graph Based Image Segmentation is a highly efficient and cost effective way to perform image segmentation. The threshold values and the number of min vertices that should be present so that a component can be considered as an image segment play an important role in determining the segmentation. The algorithm is highly efficient but it had not been effectively implemented in the project to see the effectiveness of the graph based image segmentation. 6. References [1] Pedro F. Felzenszwalb and Daniel P. Huttenlocher. Efficient Graph-Based Image Segmentation. International Journal of Computer Vision, Volume 59: , Number 2, September [2] Graph Based Image Segmentation Tutorial-Nov-21, [3] Vision-Tutorial.ppt-Nov30, chool/slides/huttenlocher.pdf