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

In this paper, we propose a new variational model to segment an object belonging to a given shape space using the active contour method, a geometric shape prior and the Mumford-Shah functional. The core of our model is an energy functional composed by three complementary terms. The first one is based on a shape model which constrains the active contour to get a shape of interest. The second term detects object boundaries from image gradients. And the third term 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 image

feature-segmentation-based registration for fast and accurate deep brain stimulation targeting

Objects Deep brain stimulation (DBS) has turned out to be the surgical technique of choice for the treatment of movement disorders, e.g. Parkinsons disease (PD), the usual target being the subthalamic nucleus (STN). The targeting of such a small structure is crucial for the outcome of the surgery. Unfortunately the STN is in general not easily distinguishable in common medical images. Material and Methods Eight bilaterally implanted PD patients were considered (16 STNs). A three-dimensional MR T1-weighted sequence and inversion recovery T2-weighted coronal slices were acquired pre-operatively. We study the influence on the STN location of several surrounding structures through a proposed methodology for the construction of a ground truth and an original validation scheme that allows evaluating performances of different targeting methods. Results The inter-expert variability in identifying the STN location is 1.61 ± 0.29 mm and 1.40 ± 0.38 mm for expert 1 and 2 respectively while the best choice of features using segmentation-based registration gives an error of 1.55 ± 0.73 mm. Conclusions By registering a binary mask of the third and lateral ventricles of the patient with its corresponding binary mask of the atlas we obtain a fast, automatic and accurate pre-operative targeting comparable to the experts variability

Image Segmentation Using Weak Shape Priors

The problem of image segmentation is known to become particularly challenging in the case of partial occlusion of the object(s) of interest, background clutter, and the presence of strong noise. To overcome this problem, the present paper introduces a novel approach segmentation through the use of "weak" shape priors. Specifically, in the proposed method, an segmenting active contour is constrained to converge to a configuration at which its geometric parameters attain their empirical probability densities closely matching the corresponding model densities that are learned based on training samples. It is shown through numerical experiments that the proposed shape modeling can be regarded as "weak" in the sense that it minimally influences the segmentation, which is allowed to be dominated by data-related forces. On the other hand, the priors provide sufficient constraints to regularize the convergence of segmentation, while requiring substantially smaller training sets to yield less biased results as compared to the case of PCA-based regularization methods. The main advantages of the proposed technique over some existing alternatives is demonstrated in a series of experiments.Comment: 27 pages, 8 figure

Robust similarity registration technique for volumetric shapes represented by characteristic functions

This paper proposes a novel similarity registration technique for volumetric shapes implicitly represented by their characteristic functions (CFs). Here, the calculation of rotation parameters is considered as a spherical crosscorrelation problem and the solution is therefore found using the standard phase correlation technique facilitated by principal components analysis (PCA).Thus, fast Fourier transform (FFT) is employed to vastly improve efficiency and robustness. Geometric moments are then used for shape scale estimation which is independent from rotation and translation parameters. It is numericallydemonstrated that our registration method is able to handle shapes with various topologies and robust to noise and initial poses. Further validation of our method is performed by registering a lung database

Interactive image segmentation based on level sets of probabilities

In this paper, we present a robust and accurate algorithm for interactive image segmentation. The level set method is clearly advantageous for image objects with a complex topology and fragmented appearance. Our method integrates discriminative classification models and distance transforms with the level set method to avoid local minima and better snap to true object boundaries. The level set function approximates a transformed version of pixelwise posterior probabilities of being part of a target object. The evolution of its zero level set is driven by three force terms, region force, edge field force, and curvature force. These forces are based on a probabilistic classifier and an unsigned distance transform of salient edges. We further propose a technique that improves the performance of both the probabilistic classifier and the level set method over multiple passes. It makes the final object segmentation less sensitive to user interactions. Experiments and comparisons demonstrate the effectiveness of our method. © 2012 IEEE.published_or_final_versio

Surface reconstruction from microscopic images in optical lithography

We propose a shape-from-shading method to reconstruct surfaces of silicon wafers from images of printed circuits taken with scanning electron microscope. Our method combines the physical model of the optical acquisition system with prior knowledge about the shapes of the patterns in the circuit. The reconstruction of the surface is formulated as an optimization problem with a combined criterion based on the irradiance equation and a shape prior that constrains the shape of the surface to agree with the expected shape of the pattern. To account for the variability of the manufacturing process, the model allows a non-linear elastic deformation between the expected patterns and the reconstructed surface. Our method provides two outputs: a reconstructed surface and a deformation field. The reconstructed surface is derived from the shading observed in the images and the prior knowledge about circuit patterns, which results in a shape-from-shading technique stable and robust to noise. The deformation field produces a mapping between the expected shape and the reconstructed surface, which provides a measure of deviation between the models and the real manufacturing process