Featureless computer vision

The central thesis of this work explores how necessary linear feature extraction is, with regard to leading approaches for classification and alignment in computer vision. Linear filters are frequently employed as a preprocessing step before optimizing some learning goal in vision such as classification or alignment. Often the choice of these filters involve both: (i) large computational and memory requirements due to increased feature size, and (ii) heuristic assumptions about what filters work best for specific applications (e.g., Gabor filters, edge filters, Haar filters. etc.). A central concept of our work is that if our learning goal can be expressed as an L2 norm, and our feature extraction step linear, then the sequential feature extraction and optimization steps can be subsumed within a single learning goal. This alternative view of linear feature extraction with respect to an L2 learning goal has a number of advantages. First, for the case of classification within the well known linear support vector machine (SVM) framework, the memory and computational overheads, typically occurring due to the high dimensionality of the feature extraction process, now disappear. From a theoretical perspective the feature extraction step can now be viewed alternatively as manipulating the margin of the SVM. We demonstrate the utility of our approach for the challenging task of expression recognition on faces. Second, for the case of alignment we demonstrate that the well known and L2 -norm based Lucas & Kanade (LK) algorithm can equally capitalize on this insight. We demonstrate that the traditional LK algorithm can be equivalently cast within the Fourier domain, an algorithm we refer to as the Fourier LK (FLK) algorithm. With this formulation, we have shown that pert-brining alignment in the high dimensional linear filter feature spaces becomes mathematically equivalent to performing alignment in the low dimensional image space, if appropriate weightings are applied in the Fourier domain. This technique renders the Fourier-LK algorithm robust to noisy artifacts like illumination in comparison to the conventional Lucas-Kanade. In both the applications mentioned above i.e. classification and alignment, our work provides an alternative interpretation for learning an SVM or running Lucas-Kanade algorithm on linear filter preprocessed images. We have demonstrated that the application of linear filters is equivalent to a manipulation of the margin, through the weighting in Fourier domain, within a linear SVM or within an alignment algorithm such as Lucas-Kanade. A more interesting question should perhaps be now: "What is the best weighting to use for my application?", and ignore the question of filtering completely. This answer on how to select/learn appropriate weighting is discussed in the later part of this thesis. Building on our previous work we show that linear filters can be interpreted as distance manipulating transforms. Using this interpretation we unify the task of linear filter learning with the discipline of distance metric learning - a hitherto overlooked link. With this link established, we demonstrate how canonical distance metric learning techniques can be used to learn linear filters. We present a formulation that allows to encode spatial constraints into the learned filter. We finally show how these constraints can dramatically increase the generalization capability of canonical distance metric learning techniques in the presence of unseen illumination and viewpoint change. The title of this thesis may be interpreted at two levels. At the algebraic level our work shows that the task of linear feature extraction can be subsumed within an L2 objective, leading to the practical disappearance of an algebraic step of feature extraction. The later part of our work removes the heuristics and guess work involved in selecting a particular class of filters. This approach is 'featureless' in a more subtle sense. It is featureless in the sense that within the domain of spatially constrained linear filters it starts off as a blank slate, free from heuristic biases, and then ends up learning application specific filter weightings. Moreover, as we stress throughout this work, that from the perspective of distance based classification or alignment, the effect of applying a filter bank is reduced to the application of a diagonal weighting in the Fourier domain. A message that we drive home, is that the individual features resulting from filters are not unique, whereas the diagonal weighting is unique and should he our focus.