In order to facilitate smooth communications with researchers in other fields including statistics, this paper investigates the meaning of “statistical methods” for geometric inference based on image feature points. We point out that statistical analysis does not make sense unless the underlying “statistical ensemble” is clearly defined. We trace back the origin of feature uncertainty to image ...

In this paper, we are interested in estimating geometric quantiles when data are obtained in a complex survey. Geometric quantiles defined by Chaudhuri (1996) are an extension of univariate quantiles in the multivariate set-up that uses the geometry of multivariate data clouds. A very important application of them is the detection of outliers in multivariate data through quantile contours. This...

Combining task and motion planning requires to interleave causal and geometric reasoning, in order to guarantee the plan to be executable in the real world. The resulting search space, which is the cross product of the symbolic search space and the geometric search space, is huge. Systematically calling a geometric reasoner while evaluating symbolic actions is costly. On the other hand, geometr...

In an industrial context, most manufactured objects are designed using CAD (Computer-Aided Design) software. For visualization, data exchange or manufacturing applications, the geometric model has to be discretized into a 3Dmesh composed of a finite number of vertices and edges. However, the initial model may sometimes be lost or unavailable. In other cases, the 3D discrete representationmay be...

A novel blind method for 3D image watermarking robust against geometric distortions is proposed. A ternary watermark is embedded in a grayscale or a color 3D volume. Construction of watermarks having appropriate structure enables fast and robust watermark detection even after several geometric distortions of the watermarked volume. Simulation results indicate the ability of the proposed method ...

Ambient isotopic approximations are fundamental for correct representation of the embedding of geometric objects in R, with a detailed geometric construction given here. Using that geometry, an algorithm is presented for efficient update of these isotopic approximations for dynamic visualization with a molecular simulation. 1 Approximation and Topology for Visualization Figure 1(a) depicts a kn...

The acquirement of ground control points (GCPs) is a basic and important step in the geometric correction of remotely sensed imagery. In particular, the spatial distribution of GCPs may affect the accuracy and quality of image correction. In this paper, both a simulation experiment and actual-image analyses are carried out to investigate the effect of the sampling design for selecting GCPs on t...

Combining geometric mechanics theory, laboratory robotic experiment, and numerical simulation, we study the locomotion in granular media of the simplest noninertial swimmer, the Purcell three-link swimmer. Using granular resistive force laws as inputs, the theory relates translation and rotation of the body to shape changes (movements of the links). This allows analysis, visualization, and pred...

A novel method for multi-bit image watermarking robust to geometric distortions is proposed. A binary watermark is embedded in a grayscale or a color host image. The ability of progressive watermark detection enables fast and robust watermark detection even after several geometric distortions of the watermarked image. The embedding of a multi-bit message and its robust decoding after the waterm...

The field of three-dimensional computer graphics has long focused on the problem of synthesizing images from geometric models. These geometric models, in combination with surface descriptions characterizing the reflective properties of each element, represent the scene that is to be rendered. Computationally, the classical computer-graphics image synthesis process is a simulation problem in whi...