Graphical Models and Image Processing最新文献

Given a simple generalized polygon $\text{A}$ of line segments and arcs that is free to move and rotate and an oriented monotone chain $\text{B}$ composed of smooth parametric curved edges, the positions and orientations for $\text{A}$ to gouge-freely contact $\text{B}$ (i.e., the contact configurations) is a C⁰ continuous surface in a three dimensional space R³. Past results either limit $\text{B}$ to be polygonal or depend on the very complicated cylindrical algebraic decomposition algorithm, which is difficult to implement in practice and does not apply to parametric curves. We address this problem by conducting a rigorous study of the geometric and topological structures of the contact configurations surface and providing the exact mathematical descriptions of the faces, edges, and vertices on this surface. A practical intersection algorithm is proposed for computing the critical curves on the contact configurations surface. In addition, an application of the contact configurations in mill-turn machining is presented.

A popular method for simplifying a surface is to repeatedly contract an edge into a vertex and take concomitant actions. In such edge contraction algorithms, the position of the new vertex plays an important role in preserving the original shape. Two methods among them are distance optimization and volume optimization. Even though the two methods were independently developed by different groups and were regarded as two different branches, we found that they are unifiable. In this paper we show that they can be expressed with the same formula, and the only differences are in the weights. We prove that volume optimization is actually a distance optimization weighted by the area of triangles adjacent to the contracted edge.

Interpolation is generally needed to visualize medical images from a limited number of sliced tomographic images such as CT. In this paper, a novel gray-scale image interpolation method, for interpolating two-dimensional images accurately and efficiently, called direction-based interpolation, is investigated. In this method, the digital image is considered a sampling of the underlying continuous function, which is also called the image field. If the image is interpolated along the isovalue curves in the image field, instead of along the coordinate axes, both the edges and the internal structures of the objects in the image are well preserved. Initially, the isovalue direction at each point is calculated from the local centered moments of the image. A specific type of image, called the direction image, is composed from the isovalue directions. Then, the direction image is interpolated into a high-resolution direction image. The isovalue curve through any point in the image field is determined from the high-resolution direction image using a path-finding technique. A high-resolution gray-scale image with satisfactory object structure is then generated by interpolating the original image linearly along the isovalue curves. Experiments on a set of CT images show that this method not only preserves the shapes of complicated structures but also has an efficient computation. The comparison between the digitally reconstructed radiographs generated from the interpolated result using the direction-based interpolation method, the traditional linear interpolation method, and the traditional cubic spline interpolation method shows the promise of the proposed method in radiation treatment planning.

The least-squares method is the most commonly used technique for fitting an ellipse through a set of points. However, it has a low breakdown point, which means that it performs poorly in the presence of outliers. We describe various alternative methods for ellipse fitting which are more robust: the Theil–Sen, least median of squares, Hilbert curve, and minimum volume estimator approaches. Testing with synthetic data demonstrates that the least median of squares is the most suitable method in terms of accuracy and robustness.

It has been shown that height field ray tracing efficiency can be improved by traversing rays in steps across evenly spaced inverted cones of empty space centered above height field cells. This approach, referred to as linear parametric height field ray tracing, has previously been extended by directionalizing the inverted cones, i.e., by allowing the opening angles of the inverted cones to vary between sectors. This paper provides a mathematical analysis of parametric ray tracing complexity as a function of cone sector width and height field resolution. Empirical data on ray tracing run-times and mean lengths of traversal steps along rays during ray tracing is presented. It is shown that parametric height field ray tracing can be substantially more efficient than other popular height field ray tracing methods when cones with narrow sectors are used.

In animating an articulated entity with motion capture data, if the reconstruction is based on forward kinematics, there could be a large error in the end-effector position. The inaccuracy becomes conspicuous when the entity makes interactions with the environment or other entities. The frames at which the end-effector position needs to be accurate are designated as “keyframes” (e.g., the impact moment in a punch). We present an algorithm that processes the original joint angle data to produce a new motion in which the end-effector error is reduced to zero at keyframes. The new motion should not be too much different from the original motion. We formulated the problem as a constrained minimization problem so that the characteristics of the original joint angle data is optimally preserved during the enhancement steps. The algorithm was applied to several examples such as boxing, kicking, and catching motions. Experiments prove that our algorithm is a valuable tool to improve captured motion especially when the end-effector trajectory contains a special goal.

Representation of real regions by corresponding digital pictures causes an inherent loss of information. There are infinitely many different real regions with an identical corresponding digital picture. So, there are limitations in the reconstruction of the originals and their properties from digital pictures. The problem which will be studied here is the impact of a digitization process on the efficiency in the reconstruction of the basic geometric properties of a planar convex region from the corresponding digital picture: position (usually described by the gravity center or centroid), orientation (usually described by the axis of the least second moment), and elongation (usually calculated as the ratio of the minimal and maximal second moments values w.r.t. the axis of the least second moment). Note that the size (area) estimation of the region (mostly estimated as the number of digital points belonging to the considered region) is a problem with an extensive history in number theory. We start with smooth convex regions, i.e., regions, whose boundaries have a continuous third-order derivative and positive curvature (at every point), and show that if such a planar convex region is represented by a binary picture with resolution r, then the mentioned features can be reconstructed with an absolute upper error bound of $\text{O}\text{(}\text{1}\text{r}{}^{\mathrm{15/11-ϵ}}\text{)≈}\text{O}\text{(}\text{1}\text{r}{}^{\mathrm{1.3636...}}\text{),}$ in the worst case. Since r is the number of pixels per unit, $\text{1}\text{r}$ is the pixel size. This result can be extended to regions which may be obtained from the previously described convex regions by finite applications of unions, intersections, or set differences. The upper error bound remains the same and converges to zero with increases in grid resolution. The given description of the speed of convergence is very sharp. Only smooth, curved regions are studied because if the considered region contains a straight section, the worst-case errors in the above estimations have $\text{1}\text{r}$ as their order of magnitude. This is a trivial result—The derivation is based on the estimation of the difference between the real moments (of the first and second order) and the corresponding discrete moments. The derived estimation can be a necessary mathematical tool in the evaluation of other procedures in the area of digital image analysis based on moment calculations.

Thinning on binary images is an iterative layer by layer erosion until only the “skeletons” of the objects are left. This paper presents an efficient parallel thinning algorithm which produces either curve skeletons or surface skeletons from 3D binary objects. It is important that a curve skeleton is extracted directly (i.e., without creating a surface skeleton). The strategy which is used is called directional: each iteration step is composed of a number of subiterations each of which can be executed in parallel. One iteration step of the proposed algorithm contains 12 subiterations instead of the usual six. The algorithm makes easy implementation possible, since deletable points are given by 3×3×3 matching templates. The topological correctness for (26, 6) binary pictures is proved.