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3 and 54 the capture range of 135 paul a viola

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Unformatted text preview: nal imaging function which predicts image intensities from object normals. In practice, however, performing photometric stereo requires the kind of detailed metric information about illumination that is only available under very controlled circumstances. One cannot use natural images where the lighting is unknown and di cult to determine. Luckily, we need not actually know G, r1, r2, F , or q. As long as they exist there will be high mutual information between any novel image and a pair of model images. This is the essence of view based EMMA alignment. We don't actually perform photometric stereo, we simply assume that it is possible. As a result a pair of images should give information about any third image. To demonstrate this approach we have built a model using the two images in Figure 5.24. Figure 5.27 shows the target image, and the nal pose obtained after alignment. Figure 5.28 shows the initial pose of the model. Technically this experiment is very similar to the MRI alignment experiment. The main di erence is that the model is constructed from a pair of model images. A sample of the model ux = u1x; u2x T is a two dimensional vector containing the intensity of the two images at location x. This is similar to the two component representation of normal used in 134 5.4. LIMITATIONS OF EMMA ALIGNMENT AI-TR 1548 Figure 5.27: Car Image and Final Pose Figure 5.28: Initial Pose of Car Model the three dimensional alignment experiments. For this experiment is 0:1. The parameters were updated for 1000 iterations at a rate of 0.002. From a set of randomized experiments we have determined that the capture range of the alignment procedure is about 40 of the length and width of the car, and 35 degrees of rotation. 5.4 Limitations of EMMA Alignment Before we complete our discussion of EMMA alignment, several important caveats must be emphasized. EMMA alignment is not a recognition procedure. Though EMMA could well play a role in recognition there are two major missing components. The rst missing component is an indexing scheme. EMMA alignment only works when the initial hypothetical pose is close" to the true pose. A number of experiments have been performed in which an empirical estimate of close" is determined see Tables 5.3 and 5.4. The capture range of 135 Paul A. Viola CHAPTER 5. ALIGNMENT EXPERIMENTS alignment is not large enough to expect that a randomly chosen transformation will converge to the true solution. As a result, some sort of additional procedure is required that can rapidly propose possible poses. Such a procedure is typically called an indexing" scheme. The second missing component is the recognition process itself. Recognition requires that a decision be made about whether the model object is really present in the image. Object recognition is very similar in concept to the problem of pattern classi cation Duda and Hart, 1973; Fukunaga, 1990. Pattern classi cation is a process by which a novel input pattern is classi ed as an example of a class. The task is di cult when the structure of the class is complex and under-speci ed. For example, determining which stocks are a good investment is a classi cation task that even the most complex classi ers, human investors, have di culty performing. Pattern classi cation can be formulated as a maximum likelihood or maximum a posteriori problem. Given a novel pattern, the likelihood of each possible class is evaluated in turn. If one class is much more likely then any other, then that class is considered the correct class. Object recognition is a similar process. Given a novel image, the likelihood of each object model is evaluated. In order that there be con dence in the classi cation, it is particularly important that the most likely model be more likely than the null hypothesis: that the image does not contain any model. The likelihood of the null hypothesis is proportional to the unconditioned likelihood of an image. As we have seen, log likelihood is closely related to entropy. As a result, EMMA can be used to de ne a classi cation procedure: the mutual information between each model and the novel image is evaluated; the model selected is the one that provides the most information about the image. What is missing is a reliable measure of the unconditioned entropy of an image i.e. the information that the null hypothesis gives us about the image. The assumption that the pixels are independent underlies the EMMA estimate of image entropy. Though it leads to inaccuracy, the independence assumption has proven su cient for alignment. This is primarily because alignment is a relative procedure. The model is adjusted so that the image is best explained. Recognition, because it is an absolute procedure, is not so forgiving. A more accurate estimate of image entropy will be required before EMMA can be used for object recognition. 136 Chapter 6 Other Applications of EMMA The theory and algorithms presented in this thesis are quite general and can in principle be applied to a variety of problems. This chapter is devoted to a description of two su...
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