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We derive analytic expressions for infinite products of random 2 x 2 matrices. The determinant of the target matrix is log-normally distributed, whereas the remainder is a surprisingly complicated function of a parameter characterizing the norm of the matrix and a parameter characterizing its skewness. The distribution may have importance as an uncommitted(More)
According to Marr's paradigm of computational vision the first process is an extraction of relevant features. The goal of this paper is to quantify and characterize the information carried by features using image-structure measured at feature-points to reconstruct images. In this way, we indirectly evaluate the concept of feature-based image analysis. The(More)
Segmentation of anatomical structures in medical images is often based on a voxel/pixel classification approach. Deep learning systems, such as convolutional neural networks (CNNs), can infer a hierarchical representation of images that fosters categorization. We propose a novel system for voxel classification integrating three 2D CNNs, which have a(More)
Manifolds are widely used to model non-linearity arising in a range of computer vision applications. This paper treats statistics on manifolds and the loss of accuracy occurring when linearizing the mani-fold prior to performing statistical operations. Using recent advances in manifold computations, we present a comparison between the non-linear analog of(More)
The importance of manifolds and Riemannian geometry is spreading to applied fields in which the need to model non-linear structure has spurred widespread interest in geometry. The transfer of interest has created demand for methods for computing classical constructs of geometry on manifolds occurring in practical applications. This paper develops initial(More)
The purpose of this report 1 is to deene optic ow for scalar and density images without using a priori knowledge other than its deening conservation principle, and to incorporate measurement duality, notably the scale-space paradigm. It is argued that the design of optic ow based applications may beneet from a manifest separation between factual image(More)
The mean is often the most important statistic of a dataset as it provides a single point that summarizes the entire set. While the mean is readily defined and computed in Euclidean spaces, no commonly accepted solutions are currently available in more complicated spaces, such as spaces of tree-structured data. In this paper we study the notion of means,(More)
Membrane trafficking is essential to fundamental processes in eukaryotic life, including cell growth and division. In plant cytokinesis, post-Golgi trafficking mediates a massive flow of vesicles that form the partitioning membrane but its regulation remains poorly understood. Here, we identify functionally redundant Arabidopsis ARF guanine-nucleotide(More)