Deep Grassmann Manifold Optimization for Computer Vision

In this work, we propose methods that advance four areas in the field of computer vision: dimensionality reduction, deep feature embeddings, visual domain adaptation, and deep neural network compression. We combine concepts from the fields of manifold geometry and deep learning to develop cutting edge methods in each of these areas. Each of the methods proposed in this work achieves state-of-the-art results in our experiments. We propose the Proxy Matrix Optimization (PMO) method for optimization over orthogonal matrix manifolds, such as the Grassmann manifold. This optimization technique is designed to be highly flexible enabling it to be leveraged in many situations where traditional manifold optimization methods cannot be used. We first use PMO in the field of dimensionality reduction, where we propose an iterative optimization approach to Principal Component Analysis (PCA) in a framework called Proxy Matrix optimization based PCA (PM-PCA). We also demonstrate how PM-PCA can be used to solve the general $L_p$-PCA problem, a variant of PCA that uses arbitrary fractional norms, which can be more robust to outliers. We then present Cascaded Projection (CaP), a method which uses tensor compression based on PMO, to reduce the number of filters in deep neural networks. This, in turn, reduces the number of computational operations required to process each image with the network. Cascaded Projection is the first end-to-end trainable method for network compression that uses standard backpropagation to learn the optimal tensor compression. In the area of deep feature embeddings, we introduce Deep Euclidean Feature Representations through Adaptation on the Grassmann manifold (DEFRAG), that leverages PMO. The DEFRAG method improves the feature embeddings learned by deep neural networks through the use of auxiliary loss functions and Grassmann manifold optimization. Lastly, in the area of visual domain adaptation, we propose the Manifold-Aligned Label Transfer for Domain Adaptation (MALT-DA) to transfer knowledge from samples in a known domain to an unknown domain based on cross-domain cluster correspondences

Accelerated Object Tracking with Local Binary Features

Multi-object tracking is a problem with wide application in modern computing. Object tracking is leveraged in areas such as human computer interaction, autonomous vehicle navigation, panorama generation, as well as countless other robotic applications. Several trackers have demonstrated favorable results for tracking of single objects. However, modern object trackers must make significant tradeoffs in order to accommodate multiple objects while maintaining real-time performance. These tradeoffs include sacrifices in robustness and accuracy that adversely affect the results. This thesis details the design and multiple implementations of an object tracker that is focused on computational efficiency. The computational efficiency of the tracker is achieved through use of local binary descriptors in a template matching approach. Candidate templates are matched to a dictionary composed of both static and dynamic templates to allow for variation in the appearance of the object while minimizing the potential for drift in the tracker. Locality constraints have been used to reduce tracking jitter. Due to the significant promise for parallelization, the tracking algorithm was implemented on the Graphics Processing Unit (GPU) using the CUDA API. The tracker\u27s efficiency also led to its implantation on a mobile platform as one of the mobile trackers that can accurately track at faster than realtime speed. Benchmarks were performed to compare the proposed tracker to state of the art trackers on a wide range of standard test videos. The tracker implemented in this work has demonstrated a higher degree of accuracy while operating several orders of magnitude faster