The polygon remains a popular graphics primitive for computer graphics application. Besides having a simple representation, computer rendering of polygons is widely supported by commercial graphics hardware and software.

Three dimensional scenes are typically modeled using a single, fixed resolution model of each geometric object. Renderings of such a model are often either slow or crude, however: slow for distant objects, where the chosen detail level is excessive, and crude for nearby objects, where the detail level is insufficient. What is needed is a multiresolution model that represents objects at multiple levels of detail. With a multiresolution model, a rendering program can choose the level of detail appropriate for the object's screen size so that less time is wasted drawing insignificant detail. The principal challenge is the development of algorithms that take a detailed model as input and automatically simplify it, while preserving appearance. Multiresolution techniques can be used to speed many applications, including real time rendering for architectural and terrain simulators, and slower, higher quality rendering for entertainment and radiosity. This paper surveys existing multiresolutio...

Given the enormous number of available methods for finding polygonal approximations to curves techniques are required to assess different algorithms. Some of the standard approaches are shown to be unsuitable if the approximations contain varying numbers of lines. Instead, we suggest assessing an algorithm's results relative to an optimal polygon, and describe a measure which combines the relative fidelity and efficiency of a curve segmentation. We use this measure to compare the application of fifteen algorithms to a curve first used by Teh and Chin [31]; their ISEs are assessed relative to the optimal ISE. In addition, using an example of pose estimation, it is shown how goal-directed evaluation can be used to select an appropriate assessment criterion.

In this paper we present a novel technique for rapidly partitioning surfaces in range images into planar patches. Essential for our segmentation method is the observation that, in a scan line, the points belonging to a planar surface form a straight line segment. On the other hand, all points on a straight line segment surely belong to the same planar surface. Based on this observation, we first divide each scan line into straight line segments and subsequently consider only the set of line segments of all scan lines as segmentation primitives. We have developed a simple link-based data structure to efficiently represent line segments and their neighborhood relationship. The principle of our segmentation method is region growing. Three neighboring line segments satisfying an optimality criterion are selected as a seed region, and then a growing is carried out around the seed region. We use a noise variance estimation to automatically set some thresholds so that the algorithm can adapt ...

In this paper we present a novel edge detection algorithm for range images based on a scan line approximation technique. Compared to the known methods in the literature, our algorithm has a number of advantages. It provides edge strength measures that have a straightforward geometric interpretation and supports a classification of edge points into several subtypes. We give a definition of optimal edge detectors and compare our algorithm to this theoretical model. By simulations we show that our algorithm has a near-optimal performance. We have carried out extensive tests using real range images acquired by three range scanners with quite different characteristics. The good results that were achieved demonstrate the robustness of our edge detection algorithm. CR Categories and Subject Descriptors: I.4.6 [Segmentation]: edge and feature detection, pixel classification; I.4.8 [Scene Analysis]: range data. General Terms: Algorithms. Additional Key Words: edge detection, scan line approxi...

Digital images have become an important source of information in the modern world of communication systems. In their raw form, digital images require a tremendous amount of memory. Many research efforts have been devoted to the problem of image compression in the last two decades. Two different compression categories must be distinguished: lossless and lossy. Lossless compression is achieved if no distortion is introduced in the coded image. Applications requiring this type of compression include medical imaging and satellite photography. For applications such as video--telephony or multimedia applications some loss of information is usually tolerated in exchange for a high compression ratio.

In this paper, we discuss the elements to be taken into account when choosing one's vectorization method. The paper is extensively based on our own implementations and tests, and concentrates on methods designed to have few, if any, parameters. 1 Introduction Vectorization, i.e. raster--to--vector conversion, has been at the center of graphics recognition problems since the beginning. Despite a lot of efforts, and many proposed solutions--- including a lot of commercial software---, we have not yet reached methods which can be considered as sufficiently stable and robust to work as standalone "black boxes". The commercial software packages solve this problem by providing their vectorization method with a number of parameters, adapted to the various categories of drawings to be processed. The user is then in control of the whole process, although families of drawings can be associated with standard sets of parameters. We believe in another way: one important factor for robustness i...

Piecewise linear (PL) image coding proceeds in three steps: 1. A digital image is converted into a 1D-signal using a scanning procedure, for example by scanning lines in a zig-zag or Hilbert order. 2. The signal is approximated by the graph of a piecewise linear function, which consists of a finite number of connected line segments. 3. Entropy encoding of the sequence of the segment end points. In this step differential coding can be used for one or both coordinate sequences of the end points. To ensure a desired approximation quality a constraint is imposed, e.g., on the root-mean-square error of the PL signal. In this paper we consider uniform approximation (L1 -distortion limited compression). Two problems are addressed: First, an optimal PL approximation in the sense of a minimal number of segments is to be obtained. Second, when entropy coding of the segments is used, how can one jointly optimize the variable length code and the PL approximation yielding a better or even minimal r...

In this paper, we present a review of our work on rate-distortion based operationally optimal vertex-based lossy shape encoding techniques. We approximate the boundary of a given shape by a low order curve, such as a polygon, and consider the problem of finding the approximation which leads to the smallest distortion for a given number of bits. We also address the dual problem of finding the approximation which leads to the smallest bit rate for a given distortion. We consider two different classes of distortion measures. The first class is based on the maximum operator (such as the maximum distance between a boundary and its approximation) and the second class is based on the summation operator (such as the total number of error pels between a boundary and its approximation). For the first class, we derive a fast and operationally optimal scheme which is based on a shortest path algorithm for a weighted directed acyclic graph. For the second class, we propose a solution approach which...

Consider the problem of processing shape information derived from a noisy source such as a digital scanner. The object is to construct a polygon or a closed curve that matches the input polygon to within a fixed error tolerance and maximizes some intuitive notion of "smoothness and simplicity". Part of this goal should be to minimize the number of inflections. The algorithm presented here finds an inflectionminimizing polygonal approximation and produces a data structure that characterizes a set of closed curves that fall within the error tolerance and minimize the number of inflections. The algorithm runs in linear time, is reasonably fast in practice, and can be implemented in low-precision integer arithmetic. 1 Introduction Important practical problems in fields such as robotics, optical character recognition, and font generation often involve extracting shape information from a digital image. The data from the image can be readily converted into polygons, but the resulting polyg...