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

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

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

Prostate Biopsy Assistance System with Gland Deformation Estimation for Enhanced Precision

Computer-assisted prostate biopsies became a very active research area during the last years. Prostate tracking makes it possi- ble to overcome several drawbacks of the current standard transrectal ultrasound (TRUS) biopsy procedure, namely the insufficient targeting accuracy which may lead to a biopsy distribution of poor quality, the very approximate knowledge about the actual location of the sampled tissues which makes it difficult to implement focal therapy strategies based on biopsy results, and finally the difficulty to precisely reach non-ultrasound (US) targets stemming from different modalities, statistical atlases or previous biopsy series. The prostate tracking systems presented so far are limited to rigid transformation tracking. However, the gland can get considerably deformed during the intervention because of US probe pres- sure and patient movements. We propose to use 3D US combined with image-based elastic registration to estimate these deformations. A fast elastic registration algorithm that copes with the frequently occurring US shadows is presented. A patient cohort study was performed, which yielded a statistically significant in-vivo accuracy of 0.83+-0.54mm.Comment: This version of the paper integrates a correction concerning the local similarity measure w.r.t. the proceedings (this typing error could not be corrected before editing the proceedings

An improved model for joint segmentation and registration based on linear curvature smoother

Image segmentation and registration are two of the most challenging tasks in medical imaging. They are closely related because both tasks are often required simultaneously. In this article, we present an improved variational model for a joint segmentation and registration based on active contour without edges and the linear curvature model. The proposed model allows large deformation to occur by solving in this way the difficulties other jointly performed segmentation and registration models have in case of encountering multiple objects into an image or their highly dependence on the initialisation or the need for a pre-registration step, which has an impact on the segmentation results. Through different numerical results, we show that the proposed model gives correct registration results when there are different features inside the object to be segmented or features that have clear boundaries but without fine details in which the old model would not be able to cope. </jats:p

A Variational Model for Object Segmentation Using Boundary Information, Statistical Shape Prior and the Mumford-Shah Functional

In this paper, we propose a variational model to segment an object belonging to a given scale space using the active contour method, a geometric shape prior and the Mumford-Shah functional. We define an energy functional composed by three complementary terms. The first one detects object boundaries from image gradients. The second term constrains the active contour to get a shape compatible with a statistical shape model of the shape of interest. And the third part drives globally the shape prior and the active contour towards a homogeneous intensity region. The segmentation of the object of interest is given by the minimum of our energy functional. This minimum is computed with the calculus of variations and the gradient descent method that provide a system of evolution equations solved with the well-known level set method. We also prove the existence of this minimum in the space of functions with bounded variation. Applications of the proposed model are presented on synthetic and medical images

Interacting Active Rectangles for Estimation of Intervertebral Disk Orientation

This paper presents a fast and efficient method to determine intervertebral disk orientation in a magnetic resonance (MR) image of the spine. The algorithm originates from active contour theory and enforces a shape constraint to avoid leaks through weak or non-existent boundaries. The method represents a vertebra as a rectangle, modeled as a semi-affine transformation applied to the unit square. A regional flow integrated along the rectangle's perimeter updates the rectangle's transformation to achieve the segmentation. Further constraints are added so that adjacent rectangles have similar orientation and scale. The orientation of a disk is then inferred from its adjacent vertebrae. Experiments show that the method is fast and effective in detecting the correct intervertebral disk orientation, which is used for transverse image planning