This paper surveys locally weighted learning, a form of lazy learning and memorybased learning, and focuses on locally weighted linear regression. The survey discusses distance functions, smoothing parameters, weighting functions, local model structures, regularization of the estimates and bias, assessing predictions, handling noisy data and outliers, improving the quality of predictions by tuning t parameters, interference between old and new data, implementing locally weighted learning e ciently, and applications of locally weighted learning. A companion paper surveys how locally weighted learning can be used in robot learning and control.

This paper describes methods and data structures used to leverage motion sequences of complex linked figures. We present a technique for interpolating between example motions derived from live motion capture or produced through traditional animation tools. These motions can be characterized by emotional expressiveness or control behaviors such as turning or going uphill or downhill. We call such parameterized motions "verbs" and the parameters that control them "adverbs." Verbs can be combined with other verbs to form a "verb graph," with smooth transitions between them, allowing an animated figure to exhibit a substantial repertoire of expressive behaviors. A combination of radial basis functions and low order polynomials is used to create the interpolation space between example motions. Inverse kinematic constraints are used to augment the interpolations in order to avoid, for example, the feet slipping on the floor during a support phase of a walk cycle. Once the verbs and...

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This paper describes a fast algorithm for scattered data interpolation and approximation. Multilevel B-splines are introduced to compute a C²-continuous surface through a set of irregularly spaced points. The algorithm makes use of a coarse-tofine hierarchy of control lattices to generate a sequence of bicubic B-spline functions whose sum approaches the desired interpolation function. Large performance gains are realized by using B-spline refinement to reduce the sum of these functions into one equivalent B-spline function. Experimental results demonstrate that high-fidelity reconstruction is possible from a selected set of sparse and irregular samples.

This paper presents new solutions to the following three problems in image morphing: feature specification, warp generation, and transition control. To reduce the burden of feature specification, we first adopt a computer vision technique called snakes. We next propose the use of multilevel free-form deformations (MFFD) to achieve C 2 -continuous and one-to-one warps among feature point pairs. The resulting technique, based on B-spline approximation, is simpler and faster than previous warp generation methods. Finally, we simplify the MFFD method to construct C 2 -continuous surfaces for deriving transition functions to control geometry and color blending . Keywords: Image metamorphosis, morphing, snakes, multilevel free-form deformation, multilevel B-spline interpolation. 1. Introduction Image metamorphosis deals with the fluid transformation from one digital image into another. This technique, commonly referred to as morphing, has found widespread use in the entertainment indu...

This paper presents a new image morphing method using a two-dimensional deformation technique which provides an intuitive model for a warp. The deformation technique derives a C

One of the most common tasks in computer animation is inverse-kinematics, or determining a joint configuration required to place a particular part of an articulated character at a particular location in global space. Inversekinematics is required at design-time to assist artists using commercial 3D animation packages, for motion capture analysis, and for run-time applications such as games. We present an efficient inverse-kinematics methodology based on the interpolation of example motions and positions. The technique is demonstrated on a number of inverse-kinematics positioning tasks for a human figure. In addition to simple positioning tasks, the method provides complete motion sequences that satisfy an inversekinematic goal. The interpolation at the heart of the algorithm allows an artist’s influence to play a major role in ensuring that the system always generates plausible results. Due to the lightweight nature of the algorithm, we can position a character at extremely high frame rates, making the technique useful for time-critical run-time applications such as games. 1. Overview A talented animator can create believable characters that spark a desired response in an audience. Believable characters,

The problem of deforming a given spatial shape is treated. There are many examples of applications in visual computing: fitting surfaces to sampled data points in space, correction of distortions in tomographic imaging, modeling of free form geometric shapes, and animating metamorphoses of geometric objects. Our solution warps the space surrounding the given shape with the effect of deforming the embedded shape, too, with a function derived with scattered data interpolation methods from the displacements of a finite set of control points that can be placed arbitrarily and adaptively. We present algorithms implementing this idea on parametric surfaces and rasterized volume data.

Barycentric coordinates for triangles are commonly used in computer graphics, geometric modelling, and other computational sciences for various purposes, because they provide a convenient way to linearly interpolate data that is given at the corners of a triangle. The concept of barycentric coordinates can also be extended in several ways to convex polygons with more than three vertices, but most of these constructions break down when used in the non-convex setting. One choice that is not limited to convex configurations are the mean value coordinates and we show that they are well-defined for arbitrary planar polygons without self-intersections. Besides many other important properties, these coordinate functions are smooth and allow an efficient and robust implementation. They are particularly useful for interpolating data that is given at the vertices of the polygons and we present several examples of their application to common problems in computer graphics and geometric modelling.

This paper describes an image metamorphosis technique to handle scattered feature constraints specified with points, polylines, and splines. Solutions to the following three problems are presented: feature specification, warp generation, and transition control. We demonstrate the use of snakes to reduce the burden of feature specification. Next, we propose the use of multilevel freeform deformations (MFFD) to compute C -continuous and one-to-one mapping functions among the specified features. The resulting technique, based on B-spline approximation, is simpler and faster than previous warp generation methods. Furthermore, it produces smooth image transformations without undesirable ripples and foldovers. Finally, we simplify the MFFD algorithm to derive transition functions to control geometry and color blending. Implementation details are furnished and comparisons among various metamorphosis techniques are presented.