Statistics for Spatial Data.

An overview of the self-organizing map algorithm, on which the papers in this issue are based, is presented in this article.

The Self-Organizing Map

One way that artists create compelling character animations is by manipulating details of a character's motion. This process is expensive and repetitive. We show that we can make such motion editing more efficient by generalizing the edits an animator makes on short sequences of motion to other sequences. Our method predicts frames for the motion using Gaussian process models of kinematics and dynamics. These estimates are combined with probabilistic inference. Our method can be used to propagate edits from examples to an entire sequence for an existing character, and it can also be used to map a motion from a control character to a very different target character. The technique shows good generalization. For example, we show that an estimator, learned from a few seconds of edited example animation using our methods, generalizes well enough to edit minutes of character animation in a high-quality fashion. Learning is interactive: An animator who wants to improve the output can provide small, correcting examples and the system will produce improved estimates of motion. We make this interactive learning process efficient and natural with a fast, full-body IK system with novel features. Finally, we present data from interviews with professional character animators that indicate that generalizing and propagating animator edits can save artists significant time and work.

Generalizing motion edits with Gaussian processes

Surface editing operations commonly require geometric details of the surface to be preserved as much as possible. We argue that geometric detail is an intrinsic property of a surface and that, consequently, surface editing is best performed by operating over an intrinsic surface representation. We provide such a representation of a surface, based on the Laplacian of the mesh, by encoding each vertex relative to its neighborhood. The Laplacian of the mesh is enhanced to be invariant to locally linearized rigid transformations and scaling. Based on this Laplacian representation, we develop useful editing operations: interactive free-form deformation in a region of interest based on the transformation of a handle, transfer and mixing of geometric details between two surfaces, and transplanting of a partial surface mesh onto another surface. The main computation involved in all operations is the solution of a sparse linear system, which can be done at interactive rates. We demonstrate the effectiveness of our approach in several examples, showing that the editing operations change the shape while respecting the structural geometric detail.

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Laplacian surface editing

We introduce Gaussian process dynamical models (GPDMs) for nonlinear time series analysis, with applications to learning models of human pose and motion from high-dimensional motion capture data. A GPDM is a latent variable model. It comprises a low-dimensional latent space with associated dynamics, as well as a map from the latent space to an observation space. We marginalize out the model parameters in closed form by using Gaussian process priors for both the dynamical and the observation mappings. This results in a nonparametric model for dynamical systems that accounts for uncertainty in the model. We demonstrate the approach and compare four learning algorithms on human motion capture data, in which each pose is 50-dimensional. Despite the use of small data sets, the GPDM learns an effective representation of the nonlinear dynamics in these spaces.

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Gaussian Process Dynamical Models for Human Motion

A common motion interpolation technique for realistic human animation is to blend similar motion samples with weighting functions whose parameters are embedded in an abstract space. Existing methods, however, are insensitive to statistical properties, such as correlations between motions. In addition, they lack the capability to quantitatively evaluate the reliability of synthesized motions. This paper proposes a method that treats motion interpolations as statistical predictions of missing data in an arbitrarily definable parametric space. A practical technique of geostatistics, called universal kriging, is then introduced for statistically estimating the correlations between the dissimilarity of motions and the distance in the parametric space. Our method statistically optimizes interpolation kernels for given parameters at each frame, using a pose distance metric to efficiently analyze the correlation. Motions are accurately predicted for the spatial constraints represented in the parametric space, and they therefore have few undesirable artifacts, if any. This property alleviates the problem of spatial inconsistencies, such as foot-sliding, that are associated with many existing methods. Moreover, numerical estimates for the reliability of predictions enable motions to be adaptively sampled. Since the interpolation kernels are computed with a linear system in real-time, motions can be interactively edited using various spatial controls.

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Geostatistical motion interpolation

Recent proliferation of motion capture systems enables motion data to be saved as an archive system, and the data are usually extracted by selecting an appropriate file by its name or annotation explaining the content of motions. Such semantic-based retrieval, however, is not suited to unstructured files that include many types of elemental motions, due to the difficulty in giving comprehensible annotations. Moreover, expected motion clips are often included as a part of entire sequences, and the data therefore should be manually clipped using some authoring tools.This paper proposes an image-based user interface for retrieving motion data using a self-organizing map for supplying recognizable icons of postures. The postures are used as keys for retrieval, and the desirable segments of the motion data can be accurately extracted by specifying and ending postures. The number of possible motion segments is flexibly controlled by changing the scope of postures used as the keys.

Motion map: image-based retrieval and segmentation of motion data

This paper proposes a psychological model for simulating pedestrian behaviors in a crowded space. Our decision-making scheme controls plausible avoidance behavior depending on the positional relations among surrounding persons, on the basis of a two-stage personal space and a virtual memory structure as proposed in social psychology. Our system determines pedestrian walking speed with the crowd density to imitate the measured data in urban engineering, and automatically generates plausible motions of the individual pedestrian by composing a locomotion graph with motion capture data. Our approach based on psychology and a variety of actual measurements can increase the accuracy of simulation at both the micro and macro levels. Copyright # 2005 John Wiley & Sons, Ltd.

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Psychological model for animating crowded pedestrians

This paper presents an approach to image coding that first paints a regularly arranged dotted pattern, using colors picked from a texture sample with features corresponding to the embedded data. It then camouflages the dotted pattern using the same texture sample while preserving quality comparable to that of existing synthesis techniques.

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Texture Synthesis for Mobile Data Communications

Data hiding techniques onto images provide tools for protecting copyright or sending secret messages, and they are currently utilized as a simple input device of a cell phone by detecting a data embedded in an image with an equipped digital camera. This paper presents a method of synthesizing texture images for embedding arbitrary data by utilizing the smart techniques of generating repetitive texture patterns through feature learning of a sample image. We extended the techniques so that a synthesized image can effectively conceal the embedded pattern, and the pattern can be robustly detected from a photographed image. We demonstrate the feasibility of our techniques using texture samples including an image scanned from real material.

Shigeru Kuriyama

Papers

Geostatistical motion interpolation

Motion map: image-based retrieval and segmentation of motion data

Psychological model for animating crowded pedestrians

Texture Synthesis for Mobile Data Communications

Data-Embeddable Texture Synthesis