1995_Viola_thesis_registrationMI

1995_Viola_thesis_registrationMI

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Unformatted text preview: : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 79 81 93 94 100 101 105 106 107 111 119 123 126 128 132 133 135 6 Other Applications of EMMA 137 7 Conclusion 147 A Appendix 151 6.1 Bias Compensation : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 137 6.2 Alignment of Line Drawings : : : : : : : : : : : : : : : : : : : : : : : : : : : 142 7.1 Related Work : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 148 7.2 A Parallel with Geometrical Alignment : : : : : : : : : : : : : : : : : : : : : 149 A.1 Gradient Descent : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 151 8 Chapter 1 Introduction This thesis is about a new information theoretic approach for solving several standing problems in computer vision and image processing. For example, this approach can be used to nd the correct alignment between a three dimensional model and an image. While alignment is a critical component of the object recognition problem, it is also useful by itself in medical and military applications. We will also describe several other applications, including an image processing application and a new form of unsupervised learning. While the form of these applications is quite di erent the underlying theory and derivations are very similar. Preliminary investigation imply that the theory presented here will have wide application. Computer vision has proven more di cult than even the most pessimistic might have predicted. While the problem has been of interest for over 30 years, progress has been painstakingly slow. Even the best computer vision systems stand in stark contrast to the human visual system: our perception of images is e ortless and robust; computer vision systems are at best slow and unreliable. Among other di culties, progress has been hampered by the sheer complexity of the relationship between image and object, which involves the object's shape, surface properties, position, and illumination. A computer vision program is faced with the task of interpreting an image of intensities. While information about the shape and location of objects is somehow embedded in these intensities, the actual intensities that arise in an image are di cult to interpret. For example, changes in illumination can radically alter the intensity and shading of an image. Though 9 Paul A. Viola CHAPTER 1. INTRODUCTION the human visual system can use shading both for recognition and image interpretation, most existing computer object recognition systems cannot. These systems throw out shading information in an e ort to obtain illumination invariance". We will present a measure for comparing objects and images that uses shading information, yet is explicitly insensitive to changes in illumination. This measure is unique in that it compares 3D object models directly to raw images. No pre-processing or edge detection is required. This image model comparison measure has been rigorously derived from information theory. Both the theory and algorithms involved are new, and are based on a e cient scheme for evaluating mutual information called EMMA1. The derivation of the the alignment procedure requires few assumptions about the nature of the imaging process. As a result the algorithms are quite general and can be used in a wide variety of imaging situations. Experiments demonstrate that this approach can align a number of complex 3D object models to real images. In addition, the same technique can be used to solve problems in medical registration. Alignment adjusts the pose of an object until the mutual information between image and object is maximized. Pose adjustment can be accomplished by ascending the gradient of mutual information. We will present an alignment procedure based on stochastic approximation that a ords a speed up of at least a factor of 500 over gradient ascent. In addition, stochastic approximation can be used to accelerate a variety of other vision applications. We will describe an existing vision application which can be accelerated by a factor of 30 using stochastic approximation. EMMA has also proven useful in a number of tasks beside alignment. For example, an entropy minimization framework that can be used to detect and correct corruption in magnetic resonance images MRI. EMMA can also be used to de ne a new form of unsupervised learning. Unsupervised learning has been popularized in the neural network literature as a scheme for simplifying the representations of complex data. EMMA can be used to nd lowdimensional projections of a high dimensional input space that are maximally informative. EMMA is a random but pronounceable subset of the letters in the words EMpirical entropy Manipulation and Analysis". 1 10 1.1. AN INTRODUCTION TO ALIGNMENT AI-TR 1548 1.1 An Introduction to Alignment The general problem of alignment entails comparing a predicted image of an object with an actual image. Given an object model and a pose coordinate...
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This note was uploaded on 02/10/2010 for the course TBE 2300 taught by Professor Cudeback during the Spring '10 term at Webber.

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