The increasing popularity of points as rendering primitives has led to a variety of different rendering algorithms, and the different implementations compare like apples to oranges. In this paper, we revisit and compare a number of recently developed point-based rendering implementations within a common testbed. Also we briefly summarize a few proposed hierarchical multiresolution point data structures and discuss their advantages. Based on a common viewdependent level-of-detail (LOD) rendering framework, we then examine different hardware accelerated point rendering algorithms. Experimental results are given with respect to performance timing and rendering quality for the different approaches. Additionally, we also compare the point-based rendering techniques to a basic triangle mesh approach.

Abstract—In this paper, we present Confetti, a novel point-based rendering approach based on object-space point interpolation of densely sampled surfaces. We introduce the concept of a transformation-invariant covariance matrix of a set of points which can efficiently be used to determine splat sizes in a multiresolution point hierarchy. We also analyze continuous point interpolation in objectspace and we define a new class of parameterized blending kernels as well as a normalization procedure to achieve smooth blending. Furthermore, we present a hardware accelerated rendering algorithm based on texture mapping and-blending as well as programmable vertex and pixel-shaders. Index Terms—Point-based rendering, multiresolution modeling, level-of-detail, hardware accelerated blending. 1

We propose a scheme for modeling point sample geometry with statistical analysis. In our scheme we depart from the current schemes that deterministically represent the attributes of each point sample. We show how the statistical analysis of a densely sampled point model can be used to improve the geometry bandwidth bottleneck and to do randomized rendering without sacrificing visual realism. We first carry out a hierarchical principal component analysis (PCA) of the model. This stage partitions the model into compact local geometries by exploiting local coherence. Our scheme handles vertex coordinates, normals, and color. The input model is reconstructed and rendered using a probability distribution derived from the PCA analysis. We demonstrate the benefits of this approach in all stages of the graphics pipeline: (1) orders of magnitude improvement in the storage and transmission complexity of point geometry, (2) direct rendering from compressed data, and (3) view-dependent randomized rendering.

Using surface splats as a rendering primitive has gained increasing attention recently due to its potential for high-performance and high-quality rendering of complex geometric models. However, as with any other rendering primitive, the processing costs are still proportional to the number of primitives that we use to represent a given object. This is why complexity reduction for point-sampled geometry is as important as it is, e.g., for triangle meshes. In this paper we present a new sub-sampling technique for dense point clouds which is specifically adjusted to the particular geometric properties of circular or elliptical surface splats. A global optimization scheme computes an approximately minimal set of splats that covers the entire surface while staying below a globally prescribed maximum error tolerance #. Since our algorithm converts pure point sample data into surface splats with normal vectors and spatial extent, it can also be considered as a surface reconstruction technique which generates a hole-free piecewise linear C continuous approximation of the input data. Here we can exploit the higher flexibility of surface splats compared to triangle meshes. Compared to previous work in this area we are able to obtain significantly lower splat numbers for a given error tolerance.

In this paper, we propose a solution to adapt the differential point rendering technique developed by Kalaiah and Varshney to implicit surfaces. Differential point rendering was initially designed for parametric surfaces as a twostage sampling process that strongly relies on an adjacency relationship for the samples, which does not naturally exist for implicit surfaces. This fact made it particularly challenging to adapt the technique to implicit surfaces. To overcome this difficulty, we extended the particle sampling technique developed by Witkin and Heckbert in order to locally account for the principal directions of curvatures of the implicit surface. The final result of our process is a curvature driven anisotropic sampling where each sample "rules" a rectangular or elliptical surrounding domain and is oriented according to the directions of maximal and minimal curvatures. As in the differential point rendering technique, these samples can then be efficiently rendered using a specific shader on a programmable GPU.

Abstract. This paper describes a method for accurate dense reconstruction of a complex scene from a small set of high-resolution unorganized still images taken by a hand-held digital camera. A fully automatic data processing pipeline is proposed. Highly discriminative features are first detected in all images. Correspondences are then found in all image pairs by wide-baseline stereo matching and used in a scene structure and camera reconstruction step that can cope with occlusion and outliers. Image pairs suitable for dense matching are automatically selected, rectified and used in dense binocular matching. The dense point cloud obtained as the union of all pairwise reconstructions is fused by local approximation using oriented geometric primitives. For texturing, every primitive is mapped on the image with the best resolution. The global structure reconstruction in the first step allows us to work with an unorganized set of images and to avoid error accumulation. By using object-centered geometric primitives we are able to preserve the flexibility of the method to describe complex free-form structures, preserve the possibility to build the dense model in an incremental way, and to retain the possibility to refine the cameras and the dense model by bundle adjustment. Results are demonstrated on partial models of a circular church and a Henri de Miller’s sculpture. We observed spatial resolution in the range of centimeters on objects of about 20 m in size. 1

We present a system for constructing 3D models of real-world objects with optically challenging surfaces. The system utilizes a new range imaging concept called multipeak range imaging, which stores multiple candidates of range measurements for each point on the object surface. The multiple measurements include the erroneous range data caused by various surface properties that are not ideal for structured-light range sensing. False measurements generated by spurious reflections are eliminated by applying a series of constraint tests. The constraint tests based on local surface and local sensor visibility are applied first to individual range images. The constraint tests based on global consistency of coordinates and visibility are then applied to all range images acquired from different viewpoints. We show the effectiveness of our method by constructing 3D models of five different optically challenging objects. To evaluate the performance of the constraint tests and to examine the effects of the parameters used in the constraint tests, we acquired the ground-truth data by painting those objects to suppress the surface-related properties that cause difficulties in range sensing. Experimental results indicate that our method significantly improves upon the traditional methods for constructing reliable 3D models of optically challenging objects.

In this paper, we propose a radiosity method for the point-sampled geometry to compute diffuse interreflection of light. Most traditional radiosity methods subdivide the surfaces of objects into small elements such as quadrilaterals. However, the point-sampled geometry includes no explicit information about surfaces, presenting a difficulty in applying the traditional approach to the point-sampled geometry. The proposed method addresses this problem by computing the interreflection without reconstructing any surfaces. The method realizes lighting simulations without losing the advantages of the point-sampled geometry. 1.

Extreme simplification and rendering of point sets

We present a novel approach for extreme simplification of point set models in the context of real-time rendering. Point sets are often rendered using simple point primitives, such as oriented discs. However efficient, simple primitives are less effective in approximating large surface areas. A large number of primitives is needed to approximate even moderately simple shapes. However, often one needs to render a simplified version of the model using only a few primitives, thus to trade accuracy for simplicity. For this goal, we propose a more complex primitive, a sort of splat, that is able to approximate a larger and more complex surface area than the well-known oriented disc. To construct our primitive, we first decompose the target surface into quasi-flat regions, using an efficient algebraic multigrid algorithm. Next, we encode these regions into splats implemented using planar support polygons textured with color and transparency information and render the splats using a special blending algorithm. Our approach combines the advantages of mesh-less point-based techniques with traditional polygon-based techniques. We demonstrate our approach on various models. 1