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

3D ball skinning using PDEs for generation of smooth tubular surfaces

We present an approach to compute a smooth, interpolating skin of an ordered set of 3D balls. By construction, the skin is constrained to be C-1 continuous, and for each ball, it is tangent to the ball along a circle of contact. Using an energy formulation, we derive differential equations that are designed to minimize the skin's surface area, mean curvature, or convex combination of both. Given an initial skin, we update the skin's parametric representation using the differential equations until convergence occurs. We demonstrate the method's usefulness in generating interpolating skins of balls of different sizes and in various configurations

A shipboard cable-hauling system for large electrical cables

An air -powered hauling machine and reeling device for use at sea with large electrical cable systems such as hydrophone arrays is described. The system may be used to haul cables from 0. 3 to 2 . 0 inch diameter. Hauling tensions up to 9 80 lbs . and speeds up to 4 30 ft/ min. are provided. The principal advantage of the system is that it does not cause the cable to bend while under tension. Reeling is accomplished under only sufficient tension to cause the cable to conform to the reel.Undersea Warfare Branch Office of Naval Research under Contracts Nonr-4029(00) NR 260-10

3D ball skinning using PDEs for generation of smooth tubular surfaces

We present an approach to compute a smooth, interpolating skin of an ordered set of 3D balls. By construction, the skin is constrained to be C1 continuous, and for each ball, it is tangent to the ball along a circle of contact. Using an energy formulation, we derive differential equations that are designed to minimize the skin’s surface area, mean curvature, or convex combination of both. Given an initial skin, we update the skin’s parametric representation using the differential equations until convergence occurs. We demonstrate the method’s usefulness in generating interpolating skins of balls of different sizes and in various configurations

Variational skinning of an ordered set of discrete 2D balls

This paper considers the problem of computing an interpolating envelope of an ordered set of 2D balls. By construction, the envelope is constrained to be C1 continuous, and for each ball, it touches the ball at a point and is tangent to the ball at the point of contact. Using an energy formulation, we derive differential equations that are designed to minimize the envelope’s arc length and/or curvature subject to these constraints. Given an initial envelope, we update the envelope’s parameters using the differential equations until convergence occurs. We demonstrate the method’s usefulness in generating interpolating envelopes of balls of different sizes and in various configurations

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

Shape-driven segmentation of the arterial wall in intravascular ultrasound images

Segmentation of arterial wall boundaries from intravascular images is an important problem for many applications in the study of plaque characteristics, mechanical properties of the arterial wall, its 3D reconstruction, and its measurements such as lumen size, lumen radius, and wall radius. We present a shape-driven approach to segmentation of the arterial wall from intravascular ultrasound images in the rectangular domain. In a properly built shape space using training data, we constrain the lumen and media-adventitia contours to a smooth, closed geometry, which increases the segmentation quality without any tradeoff with a regularizer term. In addition to a shape prior, we utilize an intensity prior through a non-parametric probability density based image energy, with global image measurements rather than pointwise measurements used in previous methods. Furthermore, a detection step is included to address the challenges introduced to the segmentation process by side branches and calcifications. All these features greatly enhance our segmentation method. The tests of our algorithm on a large dataset demonstrate the effectiveness of our approach

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

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