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Region Detection

Region Detection. The split-and-merge algorithm is a straightforward way of finding a segmentation of an image that provides homogeneity within regions and non-homogeneity of neighboring regions.

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Region Detection

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  1. Region Detection • The split-and-merge algorithm is a straightforward way of finding a segmentation of an image that provides homogeneity within regions and non-homogeneity of neighboring regions. • However, starting this algorithm with the entire image and cut it down hierarchically into quadrants can lead to unwanted results. • It is often more appropriate to identify candidate regions in the image and use them as the units in the split-and-merge algorithm. Computer Vision Lecture 16: Region Representation

  2. Region Detection • Such candidate regions could be determined through variants of thresholding. • We will always speak of brightness thresholding, but other features such as texture or color could be used as well. • As you will see, prior knowledge about the scene can be helpful for correct region detection, such as • intensity characteristics of objects, • sizes of objects, • fraction of the image occupied by objects, or • number of different types of objects in the image. Computer Vision Lecture 16: Region Representation

  3. P-Tile (Percentile) Method • If we have a good estimate for the proportion of the image occupied by objects, we can use the very simple P-Tile method. • This is possible, for example, in the case of optical character recognition, where the proportion of characters (objects) on a page does not vary a lot. • To set the threshold for separating objects and background, we first compute a histogram of the intensity values in the image. • Let us say that our estimate of the proportion of object pixels in the image is P%. Computer Vision Lecture 16: Region Representation

  4. count (100 – P)% P% 0 T 255 intensity P-Tile (Percentile) Method • We set the threshold T so that P% of the pixels (area below the curve) have below-threshold intensity. • These will be classified as objects, and the other pixels will be classified as background. Computer Vision Lecture 16: Region Representation

  5. Mode Method • If we cannot estimate the proportion of the image occupied by objects, then the P-Tile method cannot be applied. • However, if we know that the objects have approximately the same brightness which is different from the background brightness, we can use the Mode method. • Assuming that we have some Gaussian noise in our image, we expect our intensity histogram to be the sum of two normal distributions with parameters (1, 1) and (2, 2). Computer Vision Lecture 16: Region Representation

  6. count 1 2 0 T 255 intensity P-Tile (Percentile) Method • The result is the histogram shown in red. • We would like to find the valley between the two peaks to set our threshold T. Computer Vision Lecture 16: Region Representation

  7. Mode Method • Usually, the two peaks are not separated as clearly as in the previous example. • We need an appropriate algorithm to estimate the location of the valley between the two peaks. • A simple but powerful algorithm based on “peakiness detection” is given on the following slide. • It does not require a-priori information on any of the parameters 1, 1, 2 or 2. • We just have to set a value for the expected minimum intensity difference between the two peaks. Computer Vision Lecture 16: Region Representation

  8. Peakiness Detection • Find two local maxima in the histogram H that are at some minimum distance apart. Suppose these occur at gray values gi and gj. • Find the lowest point gk in the histogram H between gi and gj. • Find the peakiness, defined as min[H(gi), H(gj)]/H(gk). Use smoothing before running the algorithm to avoid division by zero. • Find the combination (gi, gj, gk) with highest peakiness. Use the value gk as the threshold value to separate the objects from the background. Computer Vision Lecture 16: Region Representation

  9. Peakiness Detection • This approach can easily be generalized to images with multiple objects having different intensity values. • For n such objects we need to determine n different thresholds T1, …, Tn. • T1 separates the background from the brightest object, T2 separates the brightest object from the second-brightest, and so on. • We can adapt our peakiness detection algorithm to estimate the optimal values for these thresholds. Computer Vision Lecture 16: Region Representation

  10. Limitations of Histogram Methods • The main disadvantage of histogram methods is their disregard of spatial information. • Obviously, spatial information is important: Pixels of similar brightness are even more likely to belong to the same object when they are spatially close to each other (surface coherence). • Therefore, it is a good idea to use threshold methods in combination with spatial techniques such as split-and-merge. Computer Vision Lecture 16: Region Representation

  11. Region Representation • Depending on the purpose of our system, we may want to represent the regions that we detected in a specific way. • There are three different basic classes of representation: • array representation, • hierarchical representation, and • symbolic representation. • We will now discuss these different approaches. Computer Vision Lecture 16: Region Representation

  12. Array Representation • The simplest way to represent regions is to use a two-dimensional array of the same size as the original image. • Each entry indicates the label of the region to which the pixel belongs. • This technique is similar to the result of component labeling in binary images. • If we have overlapping regions, we can provide a mask for each region. • A mask is a binary array in which 1-pixels belong to the region in question and 0-pixels do not. Computer Vision Lecture 16: Region Representation

  13. Hierarchical Representation • Hierarchical representation of images allows us to represent the visual information at multiple resolutions. • This is useful for a variety of tasks in computer vision. • For example, the presence and number of certain objects can be more efficiently detected at low resolution. • Then object identification can be performed at high resolution. • We will look at two techniques: pyramids and quad trees. Computer Vision Lecture 16: Region Representation

  14. Pyramids • A pyramid is a set of pixel arrays, each of which shows the same image at a different resolution. • The level 0 image at the top of the pyramid consists of only 1 pixel. • Each successive level has twice as many pixels in x and y direction as the level above it. • Therefore, an n×n image is represented by levels0 to log2n. • The following slide shows the pyramid representation of a 512×512 image. Computer Vision Lecture 16: Region Representation

  15. Pyramids Computer Vision Lecture 16: Region Representation

  16. Quad Trees • Quad trees are a method for hierarchically representing binary images. • The root of a quad tree stands for the entire image, and its 4 children represent the 4 quadrants of the image. • If a quadrant is completely white or completely black, the corresponding node is marked white or black, respectively. • Otherwise, the node is expanded, and its children represent the quadrants within the original quadrant. • This process is repeated recursively until all pixels are represented. Computer Vision Lecture 16: Region Representation

  17. Quad Trees Computer Vision Lecture 16: Region Representation

  18. Symbolic Representation • For each region, represent information such as: • enclosing rectangle • moments • compactness • mean and variance of intensity • etc. • In other words, symbolic representation of a region means that we describe its characteristics using a set of (typically numerical or categorical) parameters. Computer Vision Lecture 16: Region Representation

  19. Data Structures • How can we represent regions in computer programs? • We will look at two different approaches: Region adjacency graphs, picture trees, and super grids. • Region adjacency graphs are just undirected graphs, where each vertex represents a region. • The edges in the graph indicate which regions are adjacent to each other. Computer Vision Lecture 16: Region Representation

  20. Region Adjacency Graphs Computer Vision Lecture 16: Region Representation

  21. Picture Trees • Picture trees are a hierarchical structure for storing regions. • The rule for representation is the “is-included-in” relationship: • All child regions are included in their parent region. Computer Vision Lecture 16: Region Representation

  22. Super Grids • If we want to represent region boundaries in an array, it is unclear to which region the pixels on the boundary belong (left: image; center: boundary). • If we expand our grid (right image), the boundary can be indicated without ambiguity. Computer Vision Lecture 16: Region Representation

  23. Chain Codes • An interesting way of describing a contour is using chain codes. • A chain code is an ordered list of local orientations (directions) of a contour. • These local directions are given through the locations of neighboring pixels, so there are only eight different possibilities. • We assign each of these directions a code, e.g.: Computer Vision Lecture 16: Region Representation

  24. Chain Codes • Then we start at the first edge in the list and go clockwise around the contour. • We add the code for each edge to a list, which becomes our chain code. Computer Vision Lecture 16: Region Representation

  25. Chain Codes • What happens if in our chain code for a given contour we replace every code n with (n mod 8) + 1 ? • The contour will be rotated clockwise by 45 degrees. • We can also compute the derivative of a chain code, also referred to as difference code. • Difference codes are rotation-invariant descriptors of contours. • Some features of regions, such as their corners or areas, can be directly computed from chain or difference codes. Computer Vision Lecture 16: Region Representation

  26. Slope Representation • The slope representation of a contour (also called the -s plot) is like a chain code for continuous data. • Along the contour, we plot the tangent  versus arc length s. • Then horizontal line segments in the -s plot correspond to straight line segments in the contour. • Straight line segments at other orientations in the -s plot correspond to circular arcs in the contour. • Other segments in the -s plot correspond to other curve primitives in the contour. Computer Vision Lecture 16: Region Representation

  27. Slope Representation • Note that in this plot not the actual arc length is used, but its horizontal projection: Computer Vision Lecture 16: Region Representation

  28. Slope and Curvature Density Functions • The slope density function is the histogram of all slopes (tangent angles) in a contour. • This function can be used for recognizing objects. • We can also use the derivative of the slope representation, which we can call the curvature representation. • Its histogram is the curvature density function. • The curvature density function can also be used to recognize objects. • Its advantage is its rotation invariance, i.e., matching two curvature density functions determines similarity even if the two objects have different orientations. Computer Vision Lecture 16: Region Representation

  29. 90 180 0 Density Density Density Density 270 Square Diamond 0 0 0 0 90 90 90 90 180 180 180 180 270 270 270 270 360 360 360 360 Angle Angle Angle Angle Circle Ellipse Examples of Slope Density Functions Computer Vision Lecture 16: Region Representation

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