A General Framework for Image Kernel Engineering

Understanding image content is a long standing problem of computer science. Despite decades of research in computer vision, an effective solution to this problem does not appear to be in sight. Recent advances in the theory of learning by examples indicate that devising systems which can be trained instead of programmed to solve this problem is an interesting alternative to solutions constructed from higher level image analysis and description. In this thesis we consider a number of image understanding problems viewed as classification problems for which a certain number of input/output pairs is given. Within the statistical learning schemes we adopt (binary support vector machines and one-class support vector machines), the solution to each problem is written as a linear combination of certain functions, named kernel functions. These functions, which satisfy some specific mathematical properties, are evaluated on input pairs and encode the prior knowledge on the problem domain. Roughly speaking, kernel functions can be thought of as measuring the similarity between input pairs by extracting certain features from the raw data. In this thesis we argue for the need of finding appropriate kernel functions for building effective trainable systems. Thus, we proceed to investigate, design, implement, and validate kernels for images, or engineer kernels, in this context. In the case of images, the problem of kernel engineering cannot be easily decoupled from the choice of the image description. Therefore, we make use of different descriptions depending on the nature of the considered classification problem. For classification problems like indoor/outdoor classification we choose to represent images through histograms (color, edges, co-occurrences, etc.), while for view-based object recognition we choose grey values and/or wavelets representations. In our work we introduce and study the mathematical properties of two image kernels: the Histogram Intersection kernel and the Hausdorff kernel. The Histogram Intersection kernel, derived from a similarity measure widely used in the computer vision community for color based object recognition, is found to be a very effective kernel for describing similarities between images in high level classification problems. The Histogram Intersection kernel can be implemented efficiently and does not require the introduction of additional parameters. The Hausdorff kernel, instead, which we derive as a specialization of a larger class of kernels defined on binary strings, appears to be well suited for measuring the similarity between image patches. We show that the Hausdorff kernel can be used to boost the performances of trainable 3D object detection systems trained on positive examples only. The obtained experimental results confirm that the choice of the appropriate kernel can make the difference for a specific application. We conclude by discussing strengths and weaknesses of the approach and outlining directions for future work.