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Shape from Focus Due to the finite depth offield of optical systems (see 8), only objects which are at a proper distance appear focused in the image whereas those at other depths are blurred in proportion to their distances Algorithms to exploit this blurring effect have been developed The image is modeled as a convolution of focused images with a point spread function determined by the camera parameters and the distance of the object from the camera The depth is recovered by estimating the amount of blur in the image and using the known or estimated line spread function Such reconstruction problems are mathematically ill posed However, in some applications, especially those requiring qualitative depth information, depth from focus methods are useful Shape from Motion When images of a stationary scene are acquired using a moving camera, the displacement of the image plane coordinate of a scene point from one frame to another depends on the distance of the scene point from the camera This is thus similar to the stereo imaging described in earlier sections Alternatively, a moving object also produces motion disparity in image sequences captured by a stationary camera Such a disparity also depends upon the position and velocity of the object point Methods for recovering structure and motion of objects are described in detail in 14

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A simple intensity-based segmentation usually results in too many regions Even in images where most humans see very clear regions with constant gray value, the output of a thresholding algorithm may contain many extra regions The main reasons for this problem are high-frequency noise and a gradual transition between gray values in different regions After the initial intensity-based region segmentation, the regions may need to be refined or reformed Several approaches have been proposed for postprocessing such regions obtained from a simple segmentation approach Some of these approaches use domain-dependent knowledge, while other approaches use knowledge about the imaging process The refinement may be done interactively by a person or automatically by a computer In an automatic system, the segmentation will have to be refined based on object

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characteristics and general knowledge about the images Automatic refinement is done using a combination of split and merge operations Split and merge operations eliminate false boundaries and spurious regions by merging adjacent regions that belong to the same object, and they add missing boundaries by splitting regions that contain parts of different objects Some possible approaches for refinement include:

Current Designation (by W-number) 6 6 6 6 4 4 4 4 6 6 6 4 x x x x x x x x x x x x 6 W14 6 W20 6 W29 6 W40 4 W14 4 W20 4 W29 4 W40 6 W29 6 W40 6 W55 6 W40 x x x x x x x x x x x x W14 W20 W29 W40 W14 W20 W29 W40 W29 W40 W55 W40

Remove questionable edges Use topological properties of the regions Use shape information about objects in the scene Use semantic information about the scene

The first three approaches use only information about image intensity combined with other domain-independent characteristics of regions A discussion of approaches for region refinement follows

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The merge operation combines regions that are considered similar A highlevel merge algorithm is given in Algorithm 35 The algorithm can be adapted to any of the measures of region similarity discussed in the following sections However, when applying a simple algorithm such as this, one may still get into trouble Consider the following example We have an image with three adjacent regions A, B, and C The similarity predicate determines separately that A and B are similar and that Band C are similar However, A and C are not When merging similar regions, local decisions to merge A and B, and separately Band C, will collapse the three regions into a single region even when A and C are not similar In this case, one must take additional region characteristics into consideration before merging similar regions The most important operation in the merge algorithm is to determine the similarity between two regions Many approaches have been proposed to judge the similarity of regions Broadly, the approaches to judge the similarity are based either on the gray value of regions or on the weakness

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1 Form initial regions in the image using thresholding (or a similar approach) followed by component labeling 2 Prepare a region adjacency graph (RAG) for the image 3 For each region in an image, perform the following steps: (a) Consider its adjacent region and test to see if they are similar (b) For regions that are similar, merge them and modify the RAG 4 Repeat step 3 until no regions are merged

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