Estimation of Vector Fields in Unconstrained and Inequality Constrained Variational Problems for Segmentation and Registration

Vector fields arise in many problems of computer vision, particularly in non-rigid registration. In this paper, we develop coupled partial differential equations (PDEs) to estimate vector fields that define the deformation between objects, and the contour or surface that defines the segmentation of the objects as well. We also explore the utility of inequality constraints applied to variational problems in vision such as estimation of deformation fields in non-rigid registration and tracking. To solve inequality constrained vector field estimation problems, we apply tools from the Kuhn-Tucker theorem in optimization theory. Our technique differs from recently popular joint segmentation and registration algorithms, particularly in its coupled set of PDEs derived from the same set of energy terms for registration and segmentation. We present both the theory and results that demonstrate our approach

Learning Marginalization through Regression for Hand Orientation Inference

We present a novel marginalization method for multilayered Random Forest based hand orientation regression. The proposed model is composed of two layers, where the first layer consists of a marginalization weights regressor while the second layer contains expert regressors trained on subsets of our hand orientation dataset. We use a latent variable space to divide our dataset into subsets. Each expert regressor gives a posterior probability for assigning a given latent variable to the input data. Our main contribution comes from the regression based marginalization of these posterior probabilities. We use a Kullback-Leibler divergence based optimization for estimating the weights that are used to train our marginalization weights regressor. In comparison to the state-of-the-art of both hand orientation inference and multi-layered Random Forest marginalization, our proposed method proves to be more robust

Staged Probabilistic Regression for Hand Orientation Inference

Learning the global hand orientation from 2D monocular images is a challenging task, as the projected hand shape is affected by a number of variations. These include inter-person hand shape and size variations, intra-person pose and style variations and self-occlusion due to varying hand orientation. Given a hand orientation dataset containing these variations, a single regressor proves to be limited for learning the mapping of hand silhouette images onto the orientation angles. We address this by proposing a staged probabilistic regressor (SPORE) which consists of multiple expert regressors, each one learning a subset of variations from the dataset. Inspired by Boosting, the novelty of our method comes from the staged probabilistic learning, where each stage consists of training and adding an expert regressor to the intermediate ensemble of expert regressors. Unlike Boosting, we marginalize the posterior prediction probabilities from each expert regressor by learning a marginalization weights regressor, where the weights are extracted during training using a KullbackLeibler divergence-based optimization. We extend and evaluate our proposed framework for inferring hand orientation and pose simultaneously. In comparison to the state-of-the-art of hand orientation inference, multi-layered Random Forest marginalization and Boosting, our proposed method proves to be more accurate. Moreover, experimental results reveal that simultaneously learning hand orientation and pose from 2D monocular images significantly improves the pose classification performance

Guidewire tracking in x-ray videos of endovascular interventions

We present a novel method to track a guidewire in cardiac xray video. Using variational calculus, we derive differential equations that deform a spline, subject to intrinsic and extrinsic forces, so that it matches the image data, remains smooth, and preserves an a priori length. We analytically derive these equations from first principles, and show how they include tangential terms, which we include in our model. To address the poor contrast often observed in x-ray video, we propose using phase congruency as an image-based feature. Experimental results demonstrate the success of the method in tracking guidewires in low contrast x-ray video

Coupled PDEs for Non-Rigid Registration and Segmentation

In this paper we present coupled partial differential equations (PDEs) for the problem of joint segmentation and registration. The registration component of the method estimates a deformation field between boundaries of two structures. The desired coupling comes from two PDEs that estimate a common surface through segmentation and its non-rigid registration with a target image. The solutions of these two PDEs both decrease the total energy of the surface, and therefore aid each other in finding a locally optimal solution. Our technique differs from recently popular joint segmentation and registration algorithms, all of which assume a rigid transformation among shapes. We present both the theory and results that demonstrate the effectiveness of the approach

Graph cuts segmentation using an elliptical shape prior

We present a graph cuts-based image segmentation technique that incorporates an elliptical shape prior. Inclusion of this shape constraint restricts the solution space of the segmentation result, increasing robustness to misleading information that results from noise, weak boundaries, and clutter. We argue that combining a shape prior with a graph cuts method suggests an iterative approach that updates an intermediate result to the desired solution. We first present the details of our method and then demonstrate its effectiveness in segmenting vessels and lymph nodes from pelvic magnetic resonance images, as well as human faces

Active Polyhedron: Surface Evolution Theory Applied to Deformable Meshes

This paper presents a novel 3D deformable surface that we call an active polyhedron. Rooted in surface evolution theory, an active polyhedron is a polyhedral surface whose vertices deform to minimize a regional and/or boundarybased energy functional. Unlike continuous active surface models, the vertex motion of an active polyhedron is computed by integrating speed terms over polygonal faces of the surface. The resulting ordinary differential equations (ODEs) provide improved robustness to noise and allow for larger time steps compared to continuous active surfaces implemented with level set methods. We describe an electrostatic regularization technique that achieves global regularization while better preserving sharper local features. Experimental results demonstrate the effectiveness of an active polyhedron in solving segmentation problems as well as surface reconstruction from unorganized points

Fast pseudo-enhancement correction in CT colonography using linear shift-invariant filters

This paper presents a novel method to approximate shift-variant Gaussian filtering of an image using a set of shift-invariant Gaussian filters. This approximation affords filtering of the image using fast convolution techniques that rely on the FFT, while achieving a result that closely matches the shift-variant result. We demonstrate the method in a CT colonography application that reduces the pseudo-enhancement effect, which is a local brightening artifact in CT imaging that can result from the use of oral contrast agents. Experimental results demonstrate the effectiveness of the method and emphasize its computational efficiency

Supervised Partial Volume Effect Unmixing for Brain Tumor Characterization using Multi-voxel MR Spectroscopic Imaging

A major challenge faced by multi-voxel Magnetic Resonance Spectroscopy (MV-MRS) imaging is partial volume effect (PVE), where signals from two or more tissue types may be mixed within a voxel. This problem arises due to the low resolution data acquisition, where the size of a voxel is kept relatively large to improve the signal to noise ratio. We propose a novel supervised Signal Mixture Model (SMM), which characterizes the MV-MRS signal into normal, low grade (infiltrative) and high grade (necrotic) brain tissue types, while accounting for in-type variation. An optimization problem is solved based on differential equations, to unmix the tissue by estimating mixture coefficients corresponding to each tissue type at each voxel. This enables visualization of probability heatmaps, useful for characterizing heterogeneous tumors. Experimental results show an overall accuracy of 91.67% and 88.89% for classifying tumors into either low or high grade against histopathology, and demonstrate the method's potential for non-invasive computer-aided diagnosis