Introduction This work describes an approach to finding objects in images based on deformable shape models. Boundary finding in two and three dimensional images is enhanced both by considering the bounding contour or surface as a whole and by using model-based shape information. Boundary finding using only local information has often been frustrated by poor-contrast boundary regions due to occluding and occluded objects, adverse viewing conditions and noise. Imperfect image data can be augmented with the extrinsic information that a geometric shape model provides. In order to exploit model-based information to the fullest extent, it should be incorporated explicitly, specifically, and early in the analysis. In addition, the bounding curve or surface can be profitably considered as a whole, rather than as curve or surface segments, because it tends to result in a more consistent solution overall. These models are best suited for objects whose diversity and irregularity of shape make

Our goal is to reconstruct both the shape and reflectance properties of surfaces from multiple images. We argue that an object-centered representation is most appropriate for this purpose because it naturally accommodates multiple sources of data, multiple images (including motion sequences of a rigid object), and self-occlusions. We then present a specific objectcentered reconstruction method and its implementation. The method begins with an initial estimate of surface shape provided, for example, by triangulating the result of conventional stereo. The surface shape and reflectance properties are then iteratively adjusted to minimize an objective function that combines information from multiple input images. The objective function is a weighted sum of stereo, shading, and smoothness components, where the weight varies over the surface. For example, the stereo component is weighted more strongly where the surface projects onto highly textured areas in the images, and less strongly othe...

This paper presents a physics-based approach to anatomical surface segmentation, reconstruction, and tracking in multidimensional medical images. The approach makes use of a dynamic "balloon" model---a spherical thin-plate under tension surface spline which deforms elastically to fit the image data. The fitting process is mediated by internal forces stemming from the elastic properties of the spline and external forces which are produced from the data. The forces interact in accordance with Lagrangian equations of motion that adjust the model's deformational degrees of freedom to fit the data. We employ the finite element method to represent the continuous surface in the form of weighted sums of local polynomial basis functions. We use a quintic triangular finite element whose nodal variables include positions as well as the first and second partial derivatives of the surface. We describe a system, implemented on a high performance graphics workstation, which applies the model fitting ...

This paper presents a physics-based approach for recovering the 3D shape and tracking the motion of nonrigid objects using a 3D elastically deformable balloon model. The balloon model is based on a thin-plate under tension spline which deforms to fit visual data according to internal forces stemming from the elastic properties of the surface and external forces which are produced from the data. We employ the finite element method to represent the model as a continuous surface. We use a "natural" finite element whose nodal variables comprise the position of the surface plus its first and second partial derivatives, reflecting each of the partial derivatives that occur in the spline's strain energy functional. Hence, the model directly estimates all the information needed to measure the differential geometric properties of the fitted surface. We apply the the balloon model to the reconstruction of 3D objects with irregular shape features and demonstrate its effectiveness in extracting the left ventricular surface and tracking its nonrigid motion in dynamic CT volume images. 1

A new active contour model for finding and mapping the outer cortex in brain images is developed. A cross-section of the brain cortex is modeled as a ribbon, and a constant speed mapping of its spine is sought. A variational formulation, an associated force balance condition, and a numerical approach are proposed to achieve this goal. The primary difference between this formulation and that of snakes is in the specification of the external force acting on the active contour. A study of the uniqueness and fidelity of solutions is made through convexity and frequency domain analyses, and a criterion for selection of the regularization coefficient is developed. Examples demonstrating the performance of this method on simulated and real data are provided.

A unified framework for 3-D shape reconstruction allows us to combine image-based and geometry-based information sources. The image information is akin to stereo and shape-from-shading, while the geometric information may be provided in the form of 3-D points, 3-D features or 2-D silhouettes. A formal integration framework is critical in recovering complicated surfaces because the information from a single source is often insufficient to provide a unique answer. Our approach to shape recovery is to deform a generic object-centered 3-D representation of the surface so as to minimize an objective function. This objective function is a weighted sum of the contributions of the various information sources. We describe these various terms individually, our weighting scheme, and our optimization method. Finally, we present results on anumber of difficult images of real scenes for which a single source of information would have proved insufficient.

Deformable 3--D models are used extensively in Computer Graphics and Computer Vision for Visualization, Animation and Modeling. They can be represented either as traditional explicit surfaces, such as triangulated meshes, or as implicit surfaces. Explicit surface representations are widely accepted because they are simple to deform and render. However, for fitting purposes, they suffer from the fact that using them typically involves minimizing a non-differentiable distance function. By contrast, implicit surface representations allow fitting by minimizing a differentiable algebraic distance. However, they have not gained wide acceptance because they are harder to meaningfully deform and render.

Deformable 3--D models are used extensively in Computer Graphics and Computer Vision for Visualization, Animation and Modeling. They can be represented either as traditional explicit surfaces, such as triangulated meshes, or as implicit surfaces.

models, have been extensively used to represent the deformable 3--D models that are used to fit 3--D point and 2--D silhouette data. The resulting approaches, however, suffer from the fact that fitting typically involves finding the facets that are closest to the 3--D data points or most likely to be silhouette facets. This requires searching, which is slow, and dealing with the non-differentiability of the distance function. By contrast, implicit surface representations allow fitting without search, since one can simply evaluate a differentiable field function at every data point. However, implicit representations are not necessarily the most intuitive ones and users, such as graphics designers, tend to prefer explicit models.

This paper presents a physics-based approach to surface reconstruction using an elastically deformable "sheet" model. The model is based on a thin-plate under tension spline which deforms to fit visual data according to internal forces stemming from the elastic properties of the surface and external forces which are produced from the data. We employ the finite element method to represent the model as a continuous surface. We implement two versions of the sheet using two different finite elements. The first is a triangular, quintic finite element whose nodal variables comprise the position of the surface plus its first and second partial derivatives. This element is "natural" in the sense that the nodal variables reflect each of the partial derivatives that occur in the spline's strain energy functional. The partial derivatives are useful in measuring the differential geometric properties of the fitted surface. The second element is a rectangular, bicubic finite element whose nodal variables also include some of the partial derivatives of the surface. We apply the sheet model to the reconstruction of various 3D data sets generated by several different sensing technologies related to CAGD and terrain mapping. 1