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
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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- Spring '10
- The Land, Probability distribution, Probability theory, probability density function, Mutual Information, Paul A. Viola