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Difference and accumulative difference pictures find the areas in a scene which are changing An area is usually changing due to the movement of an object Although change detection results based on difference pictures are sensitive to noise, the areas produced by a difference picture are a good place from which to start segmentation In fact, it is possible to segment a scene with very little computation using accumulative difference pictures In this section, such an approach is discussed Let us define absolute, positive, and negative difference pictures and accumulative difference pictures as follows:
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142 SEGMENTATION USING MOTION
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(148) (149) (1410) (1411) (1412) (1413)
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if IF(x, y, 1) - F(x, y, 2) I > T
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otherwise
1 0 {
if F(x, y, 1) - F(x, y, 2) > T
otherwise
AADPn(x, y) P ADPn(x, y) N ADPn(x, y)
1 if F(x, y, 1) - F(x, y, 2) < T { 0 otherwise AADPn-1(x, y) + DP1n(x, y) P ADPn-1(x, y) + PDgn(x, y) NADPn-1(x, y) + NDP1n(x, y)
Depending on the relative intensity values of the moving object and the background being covered and uncovered, PADP and NADP provide complementary information In either the PADP or NADP, the region due to the motion of an object continues to grow after the object has been completely displaced from its projection in the reference frame, while in the other, it stops growing The area in the PADP or NADP corresponds to the area covered by the object image in the reference frame The entries in this area continue to increase in value, but the region stops growing in size Accumulative difference pictures for a synthetic scene are shown in Figure 149 A test to determine whether or not a region is still growing is needed in order to obtain a mask of an object The mask can then be obtained from the accumulative difference picture where the object's area stops growing after the object is displaced from its projection In its simplest form, this approach has one obvious limitation Masks of moving objects can be extracted only after the object has been completely displaced from its projection in the reference frame However, it appears that properties of difference and accumulative difference pictures can be used to segment images in complex situations, such as running occlusion To prevent running occlusions from disrupting segmentation, the segmentation process should not wait for an object's current position to be completely displaced from its projection in the reference frame Regions in the accumulative difference pictures can be monitored as opposed to monitoring the reference frame projections of objects Simple tests on the rate of region growth and on the presence of stale entries allow a system to determine which regions are eventually going to mature and result
CHAPTER
14 DYNAMIC
VISION
Figure 149: (a)-(c) show frames 1, 5, and 7 of a scene containing a moving object The intensity-coded positive, negative, and absolute ADPs are shown in parts (d), (e), and (f), respectively in a mask for an object in the reference frame Early determination of reference frame positions of objects, and hence, extraction of masks for objects, allows a system to take the action necessary to prevent running occlusion
Motion
Correspondence
Given two frames of a sequence, one can analyze them to determine features in each frame To determine the motion of objects, one can establish the correspondence among these features The correspondence problem in motion is similar to the correspondence problem in stereo In stereo, the major constraint used is the epipolar constraint However, in motion, other constraints must be used In the following we describe a constraint propaga-
143 MOTION CORRESPONDENCE
tion approach to solve the correspondence problem Since this approach is similar to the problem for stereo, and for historical reasons, we present the formulation similar to that for stereo Relaxation Labeling
In many applications, we are given a set of labels that may be assigned to objects that may appear in the "world" Possible relationships among different objects in this world and the conditions under which a certain set of labels mayor may not be applied to a set of objects is also known The relationships among the objects in the image may be found using techniques discussed in earlier chapters Now, based on the knowledge about the labels in the domain, proper labels must be assigned to the objects in the image This problem is called the labeling problem The labeling problem may be represented as shown in Figure 1410 Each node represents an object or entity which should be assigned a label The arcs connecting nodes represent relations between objects This figure represents the observed entities and relations among them in a given situation We have to assign labels to each entity based on the label set and the constraints among the labels for the given domain Assume that we have a processor at each node We define sets R, C, L, and P for each node The set R contains all possible relations among the nodes The set C represents the compatibility among these relations The compatability among relations helps in constraining the relationships and labels for each entity in an image The set L contains all labels that can be assigned to nodes, and the set P represents the set of possible levels that can be assigned to a node at any instant in computation Each processor knows the label of its node and all nodes which are connected to it It also knows all relations involving its node and the sets Rand C Assume that in the first iteration the possible label set Pl of node i is L for all i In other words, all nodes are assigned all possible labels initially The labeling process should then iteratively remove invalid labels from pl to give Pik+1 Since at any stage labels are discarded considering only the current labels of the node, its relations with other nodes, and the constraints, each processor has sufficient information to refine its label set Pik Thus, it is possible for all processors to work synchronously Note that at any time a processor uses only information directly available to it, that is, information pertaining
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