Octavian Soldea

A comparison of Gaussian and mean curvatures estimation methods on triangular meshes

Estimating intrinsic geometric properties of a surface from a polygonal mesh obtained from range data is an important stage of numerous algorithms in computer and robot vision, computer graphics, geometric modeling, industrial and biomedical engineering. This work considers different computational schemes for local estimation of intrinsic curvature geometric properties. Five different algorithms and their modifications were tested on triangular meshes that represent tessellations of synthetic geometric models. The results were compared with the analytically computed values of the Gaussian and mean curvatures of the non-uniform rational B-spline (NURBs) surfaces, these meshes originated from. This work manifests the best algorithms suited for that indeed different algorithms should be employed to compute the Gaussian and mean curvatures.

A comparison of Gaussian and mean curvature estimation methods on triangular meshes of range image data

Estimating intrinsic geometric properties of a surface from a polygonal mesh obtained from range data is an important stage of numerous algorithms in computer and robot vision, computer graphics, geometric modeling, and industrial and biomedical engineering. This work considers different computational schemes for local estimation of intrinsic curvature geometric properties. Four different algorithms and their modifications were tested on triangular meshes that represent tessellations of synthetic geometric models. The results were compared with the analytically computed values of the Gaussian and mean curvatures of the non-uniform rational B-spline (NURBS) surfaces from which these meshes originated. The algorithms were also tested on range images of geometric objects. The results were compared with the analytic values of the Gaussian and mean curvatures of the scanned geometric objects. This work manifests the best algorithms suited for Gaussian and mean curvature estimation, and shows that different algorithms should be employed to compute the Gaussian and mean curvatures.

Learning function-based object classification from 3D imagery

We propose a novel scheme for using supervised learning for function-based classification of objects in 3D images. During the learning process, a generic multi-level hierarchical description of object classes is constructed. The object classes are described in terms of functional components. The multi-level hierarchy is designed and constructed using a large set of signature-based reasoning and grading mechanisms. This set employs likelihood functions that are built as radial-based functions from the histograms of the object instances. During classification, a probabilistic matching measure is used to search through a finite graph to find the best assignment of geometric parts to the functional structures of each class. An object is assigned to the class that provides the highest matching value. Reuse of functional primitives in different classes enables easy expansion to new categories. We tested the proposed scheme on a database of about 1000 different 3D objects. The proposed scheme achieved high classification accuracy while using small training sets.

Global segmentation and curvature analysis of volumetric data sets using trivariate B-spline functions

This paper presents a method to globally segment volumetric images into regions that contain convex or concave (elliptic) iso-surfaces, planar or cylindrical (parabolic) iso-surfaces, and volumetric regions with saddle-like (hyperbolic) iso-surfaces, regardless of the value of the iso-surface level. The proposed scheme relies on a novel approach to globally compute, bound, and analyze the Gaussian and mean curvatures of an entire volumetric data set, using a trivariate B-spline volumetric representation. This scheme derives a new differential scalar field for a given volumetric scalar field, which could easily be adapted to other differential properties. Moreover, this scheme can set the basis for more precise and accurate segmentation of data sets targeting the identification of primitive parts. Since the proposed scheme employs piecewise continuous functions, it is precise and insensitive to aliasing.

Coupled Nonparametric Shape and Moment-Based Intershape Pose Priors for Multiple Basal Ganglia Structure Segmentation

This paper presents a new active contour-based, statistical method for simultaneous volumetric segmentation of multiple subcortical structures in the brain. In biological tissues, such as the human brain, neighboring structures exhibit co-dependencies which can aid in segmentation, if properly analyzed and modeled. Motivated by this observation, we formulate the segmentation problem as a maximum a posteriori estimation problem, in which we incorporate statistical prior models on the shapes and intershape (relative) poses of the structures of interest. This provides a principled mechanism to bring high level information about the shapes and the relationships of anatomical structures into the segmentation problem. For learning the prior densities we use a nonparametric multivariate kernel density estimation framework. We combine these priors with data in a variational framework and develop an active contour-based iterative segmentation algorithm. We test our method on the problem of volumetric segmentation of basal ganglia structures in magnetic resonance images. We present a set of 2-D and 3-D experiments as well as a quantitative performance analysis. In addition, we perform a comparison to several existent segmentation methods and demonstrate the improvements provided by our approach in terms of segmentation accuracy.

Exact and efficient computation of moments of free-form surface and trivariate based geometry

Two schemes for computing moments of free-form objects are developed and analyzed. In the first scheme, we assume that the boundary of the analyzed object is represented using parametric surfaces. In the second scheme, we represent the boundary of the object as a constant set of a trivariate function. These schemes rely on a pre-computation step which allows fast re-evaluation of the moments when the analyzed object is modified. Both schemes take advantage of a representation that is based on the B-spline blending functions.

Voxel-based discriminant map classification on brain ventricles for Alzheimer's disease

One major hallmark of the Alzheimers disease (AD) is the loss of neurons in the brain. In many cases, medical experts use magnetic resonance imaging (MRI) to qualitatively measure the neuronal loss by the shrinkage or enlargement of the structures-of-interest. Brain ventricle is one of the popular choices. It is easily detectable in clinical MR images due to the high contrast of the cerebro-spinal fluid (CSF) with the rest of the parenchyma. Moreover, atrophy in any periventricular structure will directly lead to ventricle enlargement. For quantitative analysis, volume is the common choice. However, volume is a gross measure and it cannot capture the entire complexity of the anatomical shape. Since most existing shape descriptors are complex and difficult-to-reproduce, more straightforward and robust ways to extract ventricle shape features are preferred in the diagnosis. In this paper, a novel ventricle shape based classification method for Alzheimers disease has been proposed. Training process is carried out to generate two probability maps for two training classes: healthy controls (HC) and AD patients. By subtracting the HC probability map from the AD probability map, we get a 3D ventricle discriminant map. Then a matching coefficient has been calculated between each training subject and the discriminant map. An adjustable cut-off point of the matching coefficients has been drawn for the two classes. Generally, the higher the cut-off point that has been drawn, the higher specificity can be achieved. However, it will result in relatively lower sensitivity and vice versa. The benchmarked results against volume based classification show that the area under the ROC curves for our proposed method is as high as 0.86 compared with only 0.71 for volume based classification method.

Recursive computation of moments of 2D objects represented by elliptic Fourier descriptors

This paper develops a recursive method for computing moments of 2D objects described by elliptic Fourier descriptors (EFD). To this end, Greens theorem is utilized to transform 2D surface integrals into 1D line integrals and EFD description is employed to derive recursions for moments computations. A complexity analysis is provided to demonstrate space and time efficiency of our proposed technique. Accuracy and speed of the recursive computations are analyzed experimentally and comparisons with some existing techniques are also provided.

Efficient search and verification for function based classification from real range images

In this work we propose a probabilistic model for generic object classification from raw range images. Our approach supports a validation process in which classes are verified using a functional class graph in which functional parts and their realization hypotheses are explored. The validation tree is efficiently searched. Some functional requirements are validated in a final procedure for more efficient separation of objects from non-objects. The search employs a knowledge repository mechanism that monotonically adds knowledge during the search and speeds up the classification process. Finally, we describe our implementation and present results of experiments on a database that comprises about one-hundred-and-fifty real raw range images of object instances from ten classes

Global curvature analysis and segmentation of volumetric data sets using trivariate B-spline functions

This paper presents a scheme to globally compute, bound, and analyze the Gaussian and mean curvatures of an entire volumetric data set, using a trivariate B-spline volumetric representation. The proposed scheme is not only precise and insensitive to aliasing, but also provides a method to globally segment the images into volumetric regions that contain convex or concave {elliptic) iso-surfaces, planar or cylindrical (parabolic) iso-surfaces, and volumetric regions with saddle-like (hyperbolic) iso-surfaces, regardless of the value of the iso-surface level. This scheme, which derives a new differential scalar field for a given scalar field, could easily be adapted to other differential properties.