Browsing by Subject "Covariance"
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Item Covariance based point cloud descriptors for object detection and classification(2013-08) Fehr, Duc AlexandreProcessing 3D point data is of primary interest in many areas of computer vision, including object grasping, robot navigation, and 3D object recognition. The recent introduction of cheap range sensors like the Microsoft Kinect has created a great interest in the computer vision community towards developing efficient algorithms for point cloud processing. Previously, in order to capture a point cloud, expensive specialized sensors, such as lasers or dedicated range imagers, were needed; now, range data is readily available from low-cost sensors which provide easily extractable point clouds from a depth map. From here, an interesting challenge is to find different objects in the point cloud. Various descriptors have been introduced to match features in a point cloud. Cheaper sensors are not necessarily designed to produce precise measurements, which entails that the data is not as accurate as a point cloud provided from a laser or a dedicated range finder. There have been feature descriptors that have been shown to be successful in recognizing objects from point clouds. The aim of this thesis is to introduce techniques from other domains, such as image processing, into the field of 3D point cloud processing in order to improve their rendering, recognition, and classification. Covariances have been proven to be very successful in image processing but other domains as well. This work is a first demonstration of the application of covariances in conjunction with 3D point cloud data.Item Sparse models for positive definite matrices(2015-02) Sivalingam, RavishankarSparse models have proven to be extremely successful in image processing, computer vision and machine learning. However, a majority of the effort has been focused on vector-valued signals. Higher-order signals like matrices are usually vectorized as a pre-processing step, and treated like vectors thereafter for sparse modeling. Symmetric positive definite (SPD) matrices arise in probability and statistics and the many domains built upon them. In computer vision, a certain type of feature descriptor called the region covariance descriptor, used to characterize an object or image region, belongs to this class of matrices. Region covariances are immensely popular in object detection, tracking, and classification. Human detection and recognition, texture classification, face recognition, and action recognition are some of the problems tackled using this powerful class of descriptors. They have also caught on as useful features for speech processing and recognition.Due to the popularity of sparse modeling in the vector domain, it is enticing to apply sparse representation techniques to SPD matrices as well. However, SPD matrices cannot be directly vectorized for sparse modeling, since their implicit structure is lost in the process, and the resulting vectors do not adhere to the positive definite manifold geometry. Therefore, to extend the benefits of sparse modeling to the space of positive definite matrices, we must develop dedicated sparse algorithms that respect the positive definite structure and the geometry of the manifold. The primary goal of this thesis is to develop sparse modeling techniques for symmetric positive definite matrices. First, we propose a novel sparse coding technique for representing SPD matrices using sparse linear combinations of a dictionary of atomic SPD matrices. Next, we present a dictionary learning approach wherein these atoms are themselves learned from the given data, in a task-driven manner. The sparse coding and dictionary learning approaches are then specialized to the case of rank-1 positive semi-definite matrices. A discriminative dictionary learning approach from vector sparse modeling is extended to the scenario of positive definite dictionaries. We present efficient algorithms and implementations, with practical applications in image processing and computer vision for the proposed techniques.