The use.of energy-minimizing curves, known as “snakes, ” to extract features of interest in images has been introduced by Kass, Witkhr & Terzopoulos (Znt. J. Comput. Vision 1, 1987,321-331). We present a model of deformation which solves some of the problems encountered with the original method. The external forces that push the curve to the edges are modified to give more stable results. The original snake, when it is not close enough to contours, is not attracted by them and straightens to a line. Our model makes the curve behave like a balloon which is inflated by an additional force. The initial curve need no longer be close to the solution to converge. The curve passes over weak edges and is stopped only if the edge is strong. We give examples of extracting a ventricle in medical images. We have also made a first step toward 3D object reconstruction, by tracking the extracted contour on a series of successive cross sections. 0 1991 Academic press, 1~. I.

In this paper, we develop methods to rapidly remove rough features from irregularly triangulated data intended to portray a smooth surface. The main task is to remove undesirable noise and uneven edges while retaining desirable geometric features. The problem arises mainly when creating high-fidelity computer graphics objects using imperfectly-measured data from the real world. Our approach contains three novel features: an implicit integration method to achieve efficiency, stability, and large time-steps; a scale-dependent Laplacian operator to improve the diffusion process; and finally, a robust curvature flow operator that achieves a smoothing of the shape itself, distinct from any parameterization. Additional features of the algorithm include automatic exact volume preservation, and hard and soft constraints on the positions of the points in the mesh. We compare our method to previous operators and related algorithms, and prove that our curvature and Laplacian operators have several mathematically-desirable qualities that improve the appearance of the resulting surface. In consequence, the user can easily select the appropriate operator according to the desired type of fairing. Finally, we provide a series of examples to graphically and numerically demonstrate the quality of our results.

A major unsolved problem in computer graphics is the construction and animation of realistic human facial models. Traditionally, facial models have been built painstakingly by manual digitization and animated by ad hoc parametrically controlled facial mesh deformations or kinematic approximation of muscle actions. Fortunately, animators are now able to digitize facial geometries through the use of scanning range sensors and animate them through the dynamic simulation of facial tissues and muscles. However, these techniques require considerableuser input to construct facial models of individuals suitable for animation. In this paper, we present a methodology for automating this challenging task. Starting with a structured facial mesh, we develop algorithms that automatically construct functional models of the heads of human subjects from laser-scanned range and reflectance data. These algorithms automatically insert contractile muscles at anatomically correct positions within a dynamic skin model and root them in an estimated skull structure with a hinged jaw. They also synthesize functional eyes, eyelids, teeth, and a neck and fit them to the final model. The constructed face may be animated via muscle actuations. In this way, we create the most authentic and functional facial models of individuals available to date and demonstrate their use in facial animation.

The use of energy-minimizing curves, known as "snakes" to extract features of interest in images has been introduced by Kass, Witkin and Terzopoulos [23]. A balloon model was introduced in [12] as a way to generalize and solve some of the problems encountered with the original method. We present a 3D generalization of the balloon model as a 3D deformable surface, which evolves in 3D images. It is deformed under the action of internal and external forces attracting the surface toward detected edgels by means of an attraction potential. We also show properties of energy-minimizing surfaces concerning their relationship with 3D edge points. To solve the minimization problem for a surface, two simplified approaches are shown first, defining a 3D surface as a series of 2D planar curves. Then, after comparing Finite Element Method and Finite Difference Method in the 2D problem, we solve the 3D model using the Finite Element Method yielding greater stability and faster convergence. We have a...

Abstract. Estimation techniques in computer vision applications must estimate accurate model parameters despite small-scale noise in the data, occasional large-scale measurement errors (outliers), and measurements from multiple populations in the same data set. Increasingly, robust estimation techniques, some borrowed from the statistics literature and others described in the computer vision literature, have been used in solving these parameter estimation problems. Ideally, these techniques should effectively ignore the outliers and measurements from other populations, treating them as outliers, when estimating the parameters of a single population. Two frequently used techniques are least-median of

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...

not use color information in order to focus on geometric aspects. Note how our method eliminates noise from the range image while introducing real detail. The surface normals are of the same quality or better than those from photometric stereo, while most of the low-frequency bias has been eliminated. Range scanning, manual 3D editing, and other modeling approaches can provide information about the geometry of surfaces in the form of either 3D positions (e.g., triangle meshes or range images) or orientations (normal maps or bump maps). We present an algorithm that combines these two kinds of estimates to produce a new surface that approximates both. Our formulation is linear, allowing it to operate efficiently on complex meshes commonly used in graphics. It also treats high- and low-frequency components separately, allowing it to optimally combine outputs from data sources such as stereo triangulation and photometric stereo, which have different error-vs.-frequency characteristics. We demonstrate the ability of our technique to both recover high-frequency details and avoid low-frequency bias, producing surfaces that are more widely applicable than position or orientation data alone. 1

This paper presents a technique for computing the geometry of objects with general reflectance properties from images. For surfaces with varying material properties, a full segmentation into different material types is also computed. It is assumed that the camera viewpoint is fixed, but the illumination varies over the input sequence. It is also assumed that one or more example objects with similar materials and known geometry are imaged under the same illumination conditions. Unlike most previous work in shape reconstruction, this technique can handle objects with arbitrary and spatially-varying BRDFs. Furthermore, the approach works for arbitrary distant and unknown lighting environments. Finally, almost no calibration is needed, making the approach exceptionally simple to apply.

We introduce a new method of creating smooth implicit surfaces of arbitrary manifold topology. These surfaces are described by specifying locations in 3D through which the surface should pass, and also identifying locations that are interior or exterior to the surface. A 3D implicit function is created from these constraints using a variational scattered data interpolation approach. We call the iso-surface of this function a variational implicit surface. Like other implicit surface descriptions, these surfaces can be used for CSG and interference detection, may be interactively manipulated, are readily approximated by polygonal tilings, and are easy to ray trace. A key strength is that variational implicit surfaces allow the direct specification of both the location of points on the surface and surface normals. These are two important manipulation techniques that are difficult to achieve using other implicit surface representations such as sums of spherical or ellipsoidal Gaussian functions ("blobbies"). We show that these properties make variational implicit surfaces particularly attractive for interactive sculpting using the particle sampling technique introduced by Witkin and Heckbert in [30]. Our formulation also yields a simple method for converting a polygonal model to a smooth implicit model.

This paper presents a technique for computing the geometry of objects with general reflectance properties from images. For surfaces