Image morphing, or image interpolation in the time domain, deals with the metamorphosis of one image into another. In this paper, a new class of image morphing algorithms is proposed based on the theory of optimal mass transport. The L(2) mass moving energy functional is modified by adding an intensity penalizing term, in order to reduce the undesired double exposure effect. It is an intensity-based approach and, thus, is parameter free. The optimal warping function is computed using an iterative gradient descent approach. This proposed morphing method is also extended to doubly connected domains using a harmonic parameterization technique, along with finite-element methods.

This paper presents a novel multiscale shape representation and segmentation algorithm based on the spherical wavelet transform. This work is motivated by the need to compactly and accurately encode variations at multiple scales in the shape representation in order to drive the segmentation and shape analysis of deep brain structures, such as the caudate nucleus or the hippocampus. Our proposed shape representation can be optimized to compactly encode shape variations in a population at the needed scale and spatial locations, enabling the construction of more descriptive, nonglobal, nonuniform shape probability priors to be included in the segmentation and shape analysis framework. In particular, this representation addresses the shortcomings of techniques that learn a global shape prior at a single scale of analysis and cannot represent fine, local variations in a population of shapes in the presence of a limited dataset. Specifically, our technique defines a multiscale parametric model of surfaces belonging to the same population using a compact set of spherical wavelets targeted to that population. We further refine the shape representation by separating into groups wavelet coefficients that describe independent global and/or local biological variations in the population, using spectral graph partitioning. We then learn a prior probability distribution induced over each group to explicitly encode these variations at different scales and spatial locations. Based on this representation, we derive a parametric active surface evolution using the multiscale prior coefficients as parameters for our optimization procedure to naturally include the prior for segmentation. Additionally, the optimization method can be applied in a coarse-to-fine manner. We apply our algorithm to two different brain structures, the caudate nucleus and the hippocampus, of interest in the study of schizophrenia. We show: 1) a reconstruction task of a test set to validate the expressiveness of our multiscale prior and 2) a segmentation task. In the reconstruction task, our results show that for a given training set size, our algorithm significantly improves the approximation of shapes in a testing set over the Point Distribution Model, which tends to oversmooth data. In the segmentation task, our validation shows our algorithm is computationally efficient and outperforms the Active Shape Model algorithm, by capturing finer shape details.

Averaging, filtering and interpolation of 3-D object orientation data is important in both computer vision and computer graphics, for instance to smooth estimates of object orientation and interpolate between keyframes in computer animation. In this paper we present a novel framework in which the non-linear nature of these problems is avoided by embedding the manifold of 3-D orientations into a 16-dimensional Euclidean space. Linear operations performed in the new representation can be shown to be rotation invariant, and defining a projection back to the orientation manifold results in optimal estimates with respect to the Euclidean metric. In other words, standard linear filters, interpolators and estimators may be applied to orientation data, without the need for an additional machinery to handle the non-linear nature of the problems. This novel representation also provides a way to express uncertainty in 3-D orientation, analogous to the well known tensor representation for lines and hyperplanes.

In this paper, we present two novel algorithms which produce flattened visualizations of branched physiological surfaces, such as vessels. The first approach is a conformal mapping algorithm based on the minimization of two Dirichlet functionals. From a triangulated representation of vessel surfaces, we show how the algorithm can be implemented using a finite element technique. The second method is an algorithm which adjusts the conformal mapping to produce a flattened representation of the original surface while preserving areas. This approach employs the theory of optimal mass transport. Furthermore, a new way of extracting center lines for vessel fly-throughs is provided.

We employ a conformal mapping technique to flatten tubular structures with multi-branches for visualization of MRA and CT volumetric vessel imagery. This may be used for the study of possible vessel pathology or virtual colonoscopy for polyp detection. The method is based on a discrete Laplace-Beltrami operator to flatten a tubular surface onto a planar polygonal region in an angle-preserving manner. A thinned pruned medial surface (or skeleton) is used for the vessel partition.

We apply a knowledge-based segmentation method developed for still and video images to the problem of tracking missiles and high speed projectiles. Since we are only interested in segmenting a portion of the missile (namely, the nose cone), we use our segmentation procedure as a method of adapting thresholding. The key idea is to utilize a priori knowledge about the objects present in the image, e.g. missile and background, introduced via Bayes' rule. Posterior probabilities obtained in this way are anisotropically smoothed, and the image segmentation is obtained via MAP classifications of the smoothed data. When segmenting sequences of images, the smoothed posterior probabilities of past frames are used as prior distributions in succeeding frames.

An approach for the segmentation of still and video synthetic aperture radar (SAR) images is described. A priori knowledge about the objects present in the image, e.g., target, shadow and background terrain, is introduced via Bayes' rule. Posterior probabilities obtained in this way are then anisotropically smoothed, and the image segmentation is obtained via MAP classifications of the smoothed data. When segmenting sequences of images, the smoothed posterior probabilities of past frames are used to learn the prior distributions in the succeeding frame. We show with examples from public data sets that this method provides an efficient and fast technique for addressing the segmentation of SAR data.

In this paper, we consider a novel three-dimensional (3-D) visualization technique based on surface flattening for virtual colonoscopy. Such visualization methods could be important in virtual colonoscopy because they have the potential for noninvasively determining the presence of polyps and other pathologies. Further, we demonstrate a method that presents a surface scan of the entire colon as a cine, and affords the viewer the opportunity to examine each point on the surface without distortion. We use certain angle-preserving mappings from differential geometry to derive an explicit method for flattening surfaces obtained from 3-D colon computed tomography (CT) imagery. Indeed, we describe a general method based on a discretization of the Laplace-Beltrami operator for flattening a surface into the plane in a conformal manner. From a triangulated surface representation of the colon, we indicate how the procedure may be implemented using a finite element technique, which takes into account special boundary conditions. We also provide simple formulas that may be used in a real-time cine to correct for distortion.

We give an explicit method for mapping any simply connected surface onto the sphere in a manner which preserves angles. This technique relies on certain conformal mappings from differential geometry. Our method provides a new way to automatically assign texture coordinates to complex undulating surfaces. We demonstrate a finite element method that can be used to apply our mapping technique to a triangulated geometric description of a surface.

In this paper, using certain conformal mappings from uniformization theory, we give an explicit method for flattening the brain surface in a way which preserves angles. From a triangulated surface representation of the cortex, we indicate how the procedure may be implemented using finite elements. Further, we show how the geometry of the brain surface may be studied using this approach.

A new approach for the segmentation of still and video SAR images is described. A priori knowledge about the objects present in the image, e.g., target, shadow, and background terrain, is introduced via Bayes' rule. Posterior probabilities obtained in this way are then anisotropically smoothed, and the image segmentation is obtained via MAP classifications of the smoothed data. When segmenting sequences of images, the smoothed posterior probabilities of past frames are used to learn the prior distributions in the succeeding frame. We show, via a large number of examples from public data sets, that this method provides an efficient and fast technique for addressing the segmentation of SAR data.