DOPE: Distributed Optimization for Pairwise Energies

We formulate an Alternating Direction Method of Mul-tipliers (ADMM) that systematically distributes the computations of any technique for optimizing pairwise functions, including non-submodular potentials. Such discrete functions are very useful in segmentation and a breadth of other vision problems. Our method decomposes the problem into a large set of small sub-problems, each involving a sub-region of the image domain, which can be solved in parallel. We achieve consistency between the sub-problems through a novel constraint that can be used for a large class of pair-wise functions. We give an iterative numerical solution that alternates between solving the sub-problems and updating consistency variables, until convergence. We report comprehensive experiments, which demonstrate the benefit of our general distributed solution in the case of the popular serial algorithm of Boykov and Kolmogorov (BK algorithm) and, also, in the context of non-submodular functions.Comment: Accepted at CVPR 201

Fast parallel algorithms for a broad class of nonlinear variational diffusion approaches

Variational segmentation and nonlinear diffusion approaches have been very active research areas in the fields of image processing and computer vision during the last years. In the present paper, we review recent advances in the development of efficient numerical algorithms for these approaches. The performance of parallel implement at ions of these algorithms on general-purpose hardware is assessed. A mathematically clear connection between variational models and nonlinear diffusion filters is presented that allows to interpret one approach as an approximation of the other, and vice versa. Numerical results confirm that, depending on the parametrization, this approximation can be made quite accurate. Our results provide a perspective for uniform implement at ions of both nonlinear variational models and diffusion filters on parallel architectures

Variational image regularization with Euler's elastica using a discrete gradient scheme

This paper concerns an optimization algorithm for unconstrained non-convex problems where the objective function has sparse connections between the unknowns. The algorithm is based on applying a dissipation preserving numerical integrator, the Itoh--Abe discrete gradient scheme, to the gradient flow of an objective function, guaranteeing energy decrease regardless of step size. We introduce the algorithm, prove a convergence rate estimate for non-convex problems with Lipschitz continuous gradients, and show an improved convergence rate if the objective function has sparse connections between unknowns. The algorithm is presented in serial and parallel versions. Numerical tests show its use in Euler's elastica regularized imaging problems and its convergence rate and compare the execution time of the method to that of the iPiano algorithm and the gradient descent and Heavy-ball algorithms

Automatically extracting cellular structures from images generated via electron microscopy

In this paper, we consider mathematical techniques for locating cellular structures in digital images generated via electron microscopy. We approach this problem in two steps: a pre-processing denoising stage and a segmentation stage. For image denoising, we will limit our discussion to Partial Differential Equation (PDE) based methods, primarily focusing on diffusion and total variation methods. Segmentation will also b

Variational methods and its applications to computer vision

Many computer vision applications such as image segmentation can be formulated in a ''variational'' way as energy minimization problems. Unfortunately, the computational task of minimizing these energies is usually difficult as it generally involves non convex functions in a space with thousands of dimensions and often the associated combinatorial problems are NP-hard to solve. Furthermore, they are ill-posed inverse problems and therefore are extremely sensitive to perturbations (e.g. noise). For this reason in order to compute a physically reliable approximation from given noisy data, it is necessary to incorporate into the mathematical model appropriate regularizations that require complex computations. The main aim of this work is to describe variational segmentation methods that are particularly effective for curvilinear structures. Due to their complex geometry, classical regularization techniques cannot be adopted because they lead to the loss of most of low contrasted details. In contrast, the proposed method not only better preserves curvilinear structures, but also reconnects some parts that may have been disconnected by noise. Moreover, it can be easily extensible to graphs and successfully applied to different types of data such as medical imagery (i.e. vessels, hearth coronaries etc), material samples (i.e. concrete) and satellite signals (i.e. streets, rivers etc.). In particular, we will show results and performances about an implementation targeting new generation of High Performance Computing (HPC) architectures where different types of coprocessors cooperate. The involved dataset consists of approximately 200 images of cracks, captured in three different tunnels by a robotic machine designed for the European ROBO-SPECT project.Open Acces

Energy-Based Segmentation of Very Sparse Range Surfaces

This paper describes a new segmentation technique for very sparse surfaces which is based on minimizing the energy of the surfaces in the scene. While it could be used in almost any system as part of surface reconstruction/model recovery, the algorithm is designed to be usable when the depth information is scattered and very sparse, as is generally the case with depth generated by stereo algorithms. We show results from a sequential algorithm that processes laser range-finder data or synthetic data. We then discuss a parallel implementation running on the parallel Connection Machine. The idea of segmentation by energy minimization is not new. However, prior techniques have relied on discrete regularization or Markov random fields to model the surfaces to build smooth surfaces and detect depth edges. Both of the aforementioned techniques are ineffective at energy minimization for very sparse data. In addition, this method does not require edge detection and is thus also applicable when edge information is unreliable or unavailable. Our model is extremely general; it does not depend on a model of the surface shape but only on the energy for bending a surface. Thus the surfaces can grow in a more data-directed manner. The technique presented herein models the surfaces with reproducing kernel-based splines, which can be shown to solve a regularized surface reconstruction problem. From the functional form of these splines we derive computable bounds on the energy of a surface over a given finite region. The computation of the spline, and the corresponding surface representation are quite efficient for very sparse data. An interesting property of the algorithm is that it makes no attempt to determine segmentation boundaries; the algorithm can be viewed as a classification scheme which segments the data into collections of points which are "from" the same surface. Among the significant advantages of the method is the capacity to process overlapping transparent surfaces, as well as surfaces with large occluded areas

Computerized Analysis of Magnetic Resonance Images to Study Cerebral Anatomy in Developing Neonates

The study of cerebral anatomy in developing neonates is of great importance for the understanding of brain development during the early period of life. This dissertation therefore focuses on three challenges in the modelling of cerebral anatomy in neonates during brain development. The methods that have been developed all use Magnetic Resonance Images (MRI) as source data. To facilitate study of vascular development in the neonatal period, a set of image analysis algorithms are developed to automatically extract and model cerebral vessel trees. The whole process consists of cerebral vessel tracking from automatically placed seed points, vessel tree generation, and vasculature registration and matching. These algorithms have been tested on clinical Time-of- Flight (TOF) MR angiographic datasets. To facilitate study of the neonatal cortex a complete cerebral cortex segmentation and reconstruction pipeline has been developed. Segmentation of the neonatal cortex is not effectively done by existing algorithms designed for the adult brain because the contrast between grey and white matter is reversed. This causes pixels containing tissue mixtures to be incorrectly labelled by conventional methods. The neonatal cortical segmentation method that has been developed is based on a novel expectation-maximization (EM) method with explicit correction for mislabelled partial volume voxels. Based on the resulting cortical segmentation, an implicit surface evolution technique is adopted for the reconstruction of the cortex in neonates. The performance of the method is investigated by performing a detailed landmark study. To facilitate study of cortical development, a cortical surface registration algorithm for aligning the cortical surface is developed. The method first inflates extracted cortical surfaces and then performs a non-rigid surface registration using free-form deformations (FFDs) to remove residual alignment. Validation experiments using data labelled by an expert observer demonstrate that the method can capture local changes and follow the growth of specific sulcus

Unified Heat Kernel Regression for Diffusion, Kernel Smoothing and Wavelets on Manifolds and Its Application to Mandible Growth Modeling in CT Images

We present a novel kernel regression framework for smoothing scalar surface data using the Laplace-Beltrami eigenfunctions. Starting with the heat kernel constructed from the eigenfunctions, we formulate a new bivariate kernel regression framework as a weighted eigenfunction expansion with the heat kernel as the weights. The new kernel regression is mathematically equivalent to isotropic heat diffusion, kernel smoothing and recently popular diffusion wavelets. Unlike many previous partial differential equation based approaches involving diffusion, our approach represents the solution of diffusion analytically, reducing numerical inaccuracy and slow convergence. The numerical implementation is validated on a unit sphere using spherical harmonics. As an illustration, we have applied the method in characterizing the localized growth pattern of mandible surfaces obtained in CT images from subjects between ages 0 and 20 years by regressing the length of displacement vectors with respect to the template surface.Comment: Accepted in Medical Image Analysi

Image Segmentation using PDE, Variational, Morphological and Probabilistic Methods

The research in this dissertation has focused upon image segmentation and its related areas, using the techniques of partial differential equations, variational methods, mathematical morphological methods and probabilistic methods. An integrated segmentation method using both curve evolution and anisotropic diffusion is presented that utilizes both gradient and region information in images. A bottom-up image segmentation method is proposed to minimize the Mumford-Shah functional. Preferential image segmentation methods are presented that are based on the tree of shapes in mathematical morphologies and the Kullback-Leibler distance in information theory. A thorough evaluation of the morphological preferential image segmentation method is provided, and a web interface is described. A probabilistic model is presented that is based on particle filters for image segmentation. These methods may be incorporated as components of an integrated image processed system. The system utilizes Internet Protocol (IP) cameras for data acquisition. It utilizes image databases to provide prior information and store image processing results. Image preprocessing, image segmentation and object recognition are integrated in one stage in the system, using various methods developed in several areas. Interactions between data acquisition, integrated image processing and image databases are handled smoothly. A framework of the integrated system is implemented using Perl, C++, MySQL and CGI. The integrated system works for various applications such as video tracking, medical image processing and facial image processing. Experimental results on this applications are provided in the dissertation. Efficient computations such as multi-scale computing and parallel computing using graphic processors are also presented