Visual Regression with Manifold Learning

Pei Yu

doi:https://doi.org/10.21985/n2-z6bx-nz74

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Visual Regression with Manifold Learning

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Visual Regression is a general task in the area of computer vision, with input visual data space and continuous output space. Most learning-based visual estimation tasks, where the output variables take values in continuous space, are related to visual regression. Examples of visual regression include many emerging but very difficult tasks, e.g., articulated human pose estimation, accurate gaze estimation, single-image super-resolution, age estimation from facial image, etc.', 'Visual regression still remains a very challenging task, even though large amount of research efforts have been devoted to this area for decades. When the explicit relationship between input and output is not available, the mapping from input and output needs to be learned from training dataset. However, this mapping function could be highly nonlinear and extremely complex. Traditional methods purse a holistic mapping which fits the training data, e.g., regression forests, support vector regression, regression networks. Nevertheless, this kind of methods require painstaking off-line training process. When new training data is available, it suffers awkward retraining.', 'In this thesis, we propose a novel regression framework "regression-by-searching". With the rapid growth of computational power and big data, "regression-by-searching" takes the advantage of high-quality exemplars, and shifts part of the computation from off-line to on-line. The core idea is to search similar cases when one testing input comes. By shifting computation from learning complex mapping function to searching similar cases, it is able to capture the complex mapping, as it actually performs piecewise local regression. Moreover, it is more adaptable to new training data compared with holistic regression methods.', 'Though the proposed regression framework has many advantages, there are still several challenging problems to address. One crucial issue of searching-based visual regression is visual similarity, which is one of the most fundamental problems in computer vision. When the image search gives bad matches, it could ruin the regression result. Moreover, local regression model needs to capture the structure of input space and output space, which is informative to the local regression yet very challenging to utilize.', 'In this thesis, we propose two novel methods for "regression-by-searching" paradigm. We address the issues of similarity modeling and local regression modeling from the perspective of space alignment. With approach of metric learning and novel objective of manifold alignment, the proposed methods effectively adjust the similarity metric in the input space to align with the output space. Therefore, they share similar neighborhood and space structure. One of our methods aligns the affinity structure and enables regularized reconstruction for regression. The second one investigates the possibility of aligning locally linear reconstruction weights. These methods are evaluated on two challenging and very useful regression tasks, including human pose estimation and remote gaze estimation. The superior performance over holistic regression methods demonstrates its effectiveness.

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