Conflict Neutralization on Binary Space Partitioning

The Binary Space Partitioning (BSP) tree achieves fast hidden surface removal for most practical applications where an observer can move through a scene of static objects. However, the BSP algorithm generally increases the number of polygons in a scene due to its splitting stage resulting in a detrimental effect on the priority ordering and more significantly, the display calculations (shading, lighting, shadows, etc.) of the rendering pipeline.
We present the Conflict Neutralization algorithm which attempts to reduce the number of splits more effectively than existing techniques whilst maintaining the 'standard' model of a BSP tree. Our idea is similar to Conflict Minimization proposed by Fuchs; the significant difference is that our algorithm recognizes that a polygon suitable for selection in the Minimization criterion may subsequently stop the remainder of polygons achieving some reductions in cuts—with Conflict Neutralization, such a polygon is demoted.
We compare the results of Conflict Neutralization against Conflict Minimization, the Least-crossed with Most-crossed tie-breaking criterion and our own, enhanced implementation of Conflict Minimization. We show how these techniques fall into different 'depths of analysis'.     

A comparison of three shadow volume algorithms

This paper describes and compares three different approaches to computing shadows. Each is based on the idea of shadow volumes: basic algorithm, Shadow Volume BSP Tree algorithm, and Shadow Tiling, based on 2D space subdivision. Binary Space Partition trees are used to organise the polygons in the scene in a front-toback order from the point of view of the light source, and then shadows on a polygon are computed by clipping the polygon to the shadow volumes of polygons closer to the light source. The three algorithms differ in their approach to minimising the number of comparisons of a polygon with the shadow volumes of its predecessors, and one of the algorithms represents the total shadow volume itelf by a BSP tree. The algorithms are compared analytically and statistically.     

A new partitioning method for architectural environments

Computing global illumination for complex environments in moderate time and walking through them is one of the challenges in computer graphics. To meet this goal, preprocessing is necessary. This preprocessing consists in partitioning the environment into cells and determining visibility between these cells. Most of the existing partitioning methods rely on the binary space partitioning (BSP) technique which can be easily applied to axial environments. However, for non-axial scenes, BSP has a high complexity of O (n³) in time to construct a tree of size at worst O(n²), n being the total number of input polygons. Moreover, this technique entails a large number of cells that do not necessarily fit with the topology of the environment. We propose in this paper a partitioning method which can be applied to non-axial buildings with several floors. It consists of two steps. In the first step each floor is extracted by applying a BSP technique using the most occlusive horizontal polygons for splitting. In the second step each floor is in turn partitioned with a model-based method operating in a dual 2D space. The result is a low number of cells fitting at best with the environment topology. © 1998 John Wiley & Sons, Ltd.     

Polygon visibility ordering via Voronoi diagrams

Visibility determination is one of the oldest problems in computer graphics. The visibility, in terms of back-to-front polygon visibility ordering, is determined by updating a priority list as the viewpoint moves. A new list-priority algorithm, utilizing a property of Voronoi diagrams, is proposed in this paper. The operation is in two phases. First, in a pre-processing phase the scene is divided into Voronoi cells. A sub-list associated with each cell contains references to those polygons that intersect with it. The polygons are assigned a fixed set of view-independent priority orders within the cluster. Last, an interactive phase sorts the clusters according to the depth value of each Voronoi site. The most time-consuming work is performed during the pre-processing phase that only has to be executed once for the scene. Since all the polygons in a cell are pre-computed to obtain the fixed priority order within the cluster, a relatively simple task is left in the interactive phase, which is only to sort the clusters repeatedly when the viewpoint is changed. This method contains performance benefits that make it better shaped than previous BSP based methods.     

Computing Dynamic Changes to BSP Trees

This paper investigates a new method for dynamically changing Binary Space Partition (BSP) trees. A BSP tree representation of a 3D polygonal scene provides an ideal data structure for rapidly performing the hidden surface computations involved in changing the viewpoint. However, BSP trees have generally been thought to be unsuitable for applications where the geometry of objects in the scene changes dynamically. The purpose of this paper is to introduce a dynamic BSP tree algorithm which does allow for such changes, and which maintains the simplicity and integrity of the BSP tree representation. The algorithm is extended to include dynamic changes to shadows. We calibrate the algorithms by transforming a range of objects in a scene, and reporting on the observed timing results.     

基于BSP树的启发式阴影生成算法

阴影的生成在虚拟现实领域一直是个难题,特别是针对动态光源的大规模场景,目前还没有较成熟的阴影算法。通过对现有阴影生成算法和场景组织算法的研究,该文提出了基于二维空间分割树(BSP树)的启发式阴影生成算法:首先创建场景BSP树,随着观察者视点的改变,选取视剪裁体内的节点创建以光源为视点的遮挡体BSP树,然后通过对该BSP树的遍历拣选出阴影启发区内的物体,经过处理后BSP树只留下一些生成阴影必要的多边形大大减少了计算量,最后能够快速生成阴影。     

基于深度缓存和BSP树技术的表面消隐技术研究

主要介绍了两种消隐技术,深度缓存算法是通过两个缓存来实现的,其中的一个是用来存放颜色的颜色缓存器,而另一个是用来存放深度的深度缓存器。BSP就是二叉空间分区树,将视景中要显示的多边形或者实物,使用二叉树的原理组织成一种数据结构,通过这种数据结构存储多边形(实物)。     

A Statistical Comparison of Two Hidden Surface Techniques: the Scan-line and Z-buffer Algorithms

This paper compares two image space hidden surface removal algorithms for polygonal scenes. These are the z-buffer and scan-line algorithms. There is first an overview of each algorithm, followed by a simulation experiment, designed to compare the number of polygons per second which can be rendered by each algorithm. The simulation varies the number of polygons in the scene, and the size and distribution of polygons over the display. The results suggest that the z-buffer is preferred for a large enough number of polygons, however, smaller polygons and uniform distribution of polygons favour the scan-line approach. The analysis does not take into account the complexity of the shading rule, which is likely also to favour the scan-line method.     

Automatic View Selection Using Viewpoint Entropy and its Application to Image-Based Modelling

In the last decade a new family of methods, namely Image‐Based Rendering, has appeared. These techniques rely on the use of precomputed images to totally or partially substitute the geometric representation of the scene. This allows to obtain realistic renderings even with modest resources. The main problem is the amount of data needed, mainly due to the high redundancy and the high computational cost of capture. In this paper we present a new method to automatically determine the correct camera placement positions in order to obtain a minimal set of views for Image‐Based Rendering. The input is a 3D polyhedral model including textures and the output is a set of views that sample all visible polygons at an appropriate rate. The viewpoints should cover all visible polygons with an adequate quality, so that we sample the polygons at sufficient rate. This permits to avoid the excessive redundancy of the data existing in several other approaches. We also reduce the cost of the capturing process, as the number of actually computed reference views decreases. The localization of interesting viewpoints is performed with the aid of an information theory‐based measure, dubbed viewpoint entropy. This measure is used to determine the amount of information seen from a viewpoint. Next we develop a greedy algorithm to minimize the number of images needed to represent a scene. In contrast to other approaches, our system uses a special preprocess for textures to avoid artifacts appearing in partially occluded textured polygons. Therefore no visible detail of these images is lost. ACM CSS: I.3.7 Computer Graphics—Three‐Dimensional Graphics and Realism     

Automatic Camera Placement for Image-Based Modeling

We present an automatic camera placement method for generating image-based models from scenes with known geometry. Our method first approximately determines the set of surfaces visible from a given viewing area and then selects a small set of appropriate camera positions to sample the scene from. We define a quality measure for a surface as seen, or covered, from the given viewing area. Along with each camera position, we store the set of surfaces which are best covered by this camera. Next, one reference view is generated from each camera position by rendering the scene. Pixels in each reference view that do not belong to the selected set of polygons are masked out.
The image-based model generated by our method, covers every visible surface only once, associating it with a camera position from which it is covered with quality that exceeds a user-specified quality threshold. The result is a compact non-redundant image-based model with controlled quality.
The problem of covering every visible surface with a minimum number of cameras (guards) can be regarded as an extension to the well-known Art Gallery Problem. However, since the 3D polygonal model is textured, the camera-polygon visibility relation is not binary; instead, it has a weight — the quality of the polygon's coverage.     

基于点索引的网格模型的层次结构

针对稠密采样的网格模型．提出一种基于面片中心点索引的新的场景BSP树结构．与常规RSP树构造方式不同,文中RSP树以面片中心点位置作为场景中各面片二叉分类的依据,避免了常规BSP树构造方法中因分割与削分平面相交的面片引起的场景复杂度的增加,大大简化了BSP树的构造过程．实验结果表明：对稠密网格场景,文中的BSP树比常规方式构造的BSP树任加速光线跟踪算法中的求交测试具有明显的优势．     

Improved Binary Space Partition merging

This paper presents a new method for evaluating boolean set operations between Binary Space Partition (BSP) trees. Our algorithm has many desirable features, including both numerical robustness and O(n) output sensitive time complexity, while simultaneously admitting a straightforward implementation. To achieve these properties, we present two key algorithmic improvements. The first is a method for eliminating null regions within a BSP tree using linear programming. This replaces previous techniques based on polygon cutting and tree splitting. The second is an improved method for compressing BSP trees based on a similar approach within binary decision diagrams. The performance of the new method is analyzed both theoretically and experimentally. Given the importance of boolean set operations, our algorithms can be directly applied to many problems in graphics, CAD and computational geometry.     

Binary-space-partitioned images for resolving image-based visibility

We propose a novel 2D representation for 3D visibility sorting, the binary-space-partitioned image (BSPI), to accelerate real-time image-based rendering. BSPI is an efficient 2D realization of a 3D BSP tree, which is commonly used in computer graphics for time-critical visibility sorting. Since the overall structure of a BSP tree is encoded in a BSPI, traversing a BSPI is comparable to traversing the corresponding BSP tree. BSPI performs visibility sorting efficiently and accurately in the 2D image space by warping the reference image triangle-by-triangle instead of pixel-by-pixel. Multiple BSPIs can be combined to solve "disocclusion," when an occluded portion of the scene becomes visible at a novel viewpoint. Our method is highly automatic, including a tensor voting preprocessing step that generates candidate image partition lines for BSPIs, filters the noisy input data by rejecting outliers, and interpolates missing information. Our system has been applied to a variety of real data, including stereo, motion, and range images.     

基于主要遮挡物的动态可见性算法

对景物密集的复杂场景 ,提出了基于主要遮挡物的动态可见性算法 .该算法通过场景中预先定义的主要遮挡物 ,动态地形成一个遮挡树 ,位于遮挡树遮挡区域中的景物将被剔除 .当场景按照 BSP树组织 ,并按从前向后的顺序绘制场景时 ,算法具有高效率 .对主要遮挡物采用简化的遮挡物代理 ,对盒子类型的遮挡物提出了一种有效的简化算法 .该算法已经被“RTG三维图形开发工具包”采用 ,经实际验证 ,对复杂场景 ,该算法可以明显地提高绘制速度     

基于凸剖分的多边形窗口线裁剪算法

以不增加新点的方式将多边形剖分为一些凸多边形,并基于这些多边形的边建立二叉树进行管理.裁剪计算时,根据二叉树快速地找到与被裁剪线有相交的凸多边形,然后运用高效的凸多边形裁剪算法进行线裁剪.该方法能自适应地降低裁剪计算的复杂度,使其在O(logn)和O(n)之间变化,并在大多数情况下小于O(n),其中n是多边形边数.虽然该方法需要进行预处理,但在许多应用(如多边形窗口对多边形的裁剪)中,其总执行时间(包括预处理时间和裁剪时间)比已有的不需要预处理的裁剪算法少很多.     

The contour problem for rectilinear polygons

The union of a set of p, not necessarily disjoint, rectilinear polygons in the plane determines a set of disjoint rectilinear polygons. We present an O(n log n + e) time and O(n) space algorithm to compute the edges of the disjoint polygons, that is, the contour, where n is the total number of vertices in the original polygons and e the total number in the resulting set. This time-and space-optimal algorithm uses the scan-line paradigm as in two previous approaches to this problem for rectangles, but requires a simpler data structure. Moreover, if the given rectilinear polygons are rectilinear convex, the space requirement is reduced to O(p).     

Impact of training and validation sample selection on classification accuracy and accuracy assessment when using reference polygons in object-based classification

Reference polygons are homogenous areas that aim to provide the best available assessment of ground condition that the user can identify. Delineation of such polygons provides a convenient and efficient approach for researchers to identify training and validation data for supervised classification. However, the spatial dependence of training and validation data should be taken into account when the two data sets are obtained from a common set of reference polygons. We investigate the effect on classification accuracy and the accuracy estimates derived from the validation data when training and validation data are obtained from four selection schemes. The four schemes are composed of two sampling designs (simple random and systematic) and two methods for splitting sample points between training and validation (validation points in separate polygons from training points and validation points and training points split within the same polygons). A supervised object-based classification of the study region was repeated 30 times for each selection scheme. The selection scheme did not impact classification accuracy, but estimates of overall (OA), user's (UA), and producer's (PA) accuracies produced from the validation data overestimated accuracy for the study region by about 10%. The degree of overestimation was slightly greater when the validation sample points were allowed to be in the same polygons as the training data points. These results suggest that accuracy estimates derived from splitting training and validation within a limited set of reference polygons should be regarded with suspicion. To be fully confident in the validity of the accuracy estimates, additional validation sample points selected from the region outside the reference polygons may be needed to augment the validation sample selected from the reference polygons.     

Parallel dynamic programming

Recurrence formulations for various problems, such as finding an optimal order of matrix multiplication, finding an optimal binary search tree, and optimal triangulation of polygons, assume a similar form. A. Gibbons and W. Rytter (1988) gave a CREW PRAM algorithm to solve such dynamic programming problems. The algorithm uses O(n⁶/log n) processors and runs in O(log² n) time. In this article, a modified algorithm is presented that reduces the processor requirement to O(n⁶/log ⁵n) while maintaining the same time complexity of O(log² n)     

Recognition of writers by handwriting images

The objective of this paper is the automatic identification of individual persons by means of their handwriting images. The image, digitized by a computer-controlled TV-camera, is analyzed in two different ways. In terms of the writing process, it is first interpreted as a set of lines, which have to be reconstructed by methods of scene analysis.

Secondly, a special non-linear transformation is applied to the image, which provides features representing global statistical information about the image. In a classification experiment involving 20 writers (40 samples of each), 797 out of 800 samples were identified correctly.     

A Scanline Method for Solid Model Display

The modelling of solid objects is becoming increasingly important in the application of computer graphics to a wide variety of problems, such as CAD/CAM, simulation, and molecular modelling. A variety of methods for rendering solid objects exists, including 2-Buffer, Scanline and Ray Tracing. This paper is concerned with a scanline method for the production of still images of complex objects. The implementation of a scanline algorithm is discussed, in conjunction with a consideration of its performance in relation to the z-buffer method.
Many scanline methods cater only for a restricted class of primitives, such as polygons or spheres, whereas this implementation is a general purpose scanline algorithm capable of being extended to handle a variety of primitives. The primitives currently available are polygons, spheres, spheres swept along straight-line trajectories, and cylinders. Polygonal models of cubes, cones and cylinders are also available.
The approach is capable of dealing with "positive" and "negative" volumes, allowing objects with holes to be modelled and displayed. It has further been extended to cater for the inclusion of transparent objects into a scene, and consequently allows the modelling of coloured "glass" objects.