Charles T. Loop

Computing rectifying homographies for stereo vision

Image rectification is the process of applying a pair of 2D projective transforms, or homographies, to a pair of images whose epipolar geometry is known so that epipolar lines in the original images map to horizontally aligned lines in the transformed images. We propose a novel technique for image rectification based on geometrically well defined criteria such that image distortion due to rectification is minimized. This is achieved by decomposing each homography into a specialized projective transform, a similarity transform, followed by a shearing transform. The effect of image distortion at each stage is carefully considered.

Resolution independent curve rendering using programmable graphics hardware

We present a method for resolution independent rendering of paths and bounded regions, defined by quadratic and cubic spline curves, that leverages the parallelism of programmable graphics hardware to achieve high performance. A simple implicit equation for a parametric curve is found in a space that can be thought of as an analog to texture space. The image of a curves Bezier control points are found in this space and assigned to the control points as texture coordinates. When the triangle(s) corresponding to the Bezier curve control hull are rendered, a pixel shader program evaluates the implicit equation for a pixels interpolated texture coordinates to determine an inside/outside test for the curve. We extend our technique to handle anti-aliasing of boundaries. We also construct a vector image from mosaics of triangulated Bezier control points and show how to deform such images to create resolution independent texture on three dimensional objects.

Approximating Catmull-Clark subdivision surfaces with bicubic patches

We present a simple and computationally efficient algorithm for approximating Catmull-Clark subdivision surfaces using a minimal set of bicubic patches. For each quadrilateral face of the control mesh, we construct a geometry patch and a pair of tangent patches. The geometry patches approximate the shape and silhouette of the Catmull-Clark surface and are smooth everywhere except along patch edges containing an extraordinary vertex where the patches are C0. To make the patch surface appear smooth, we provide a pair of tangent patches that approximate the tangent fields of the Catmull-Clark surface. These tangent patches are used to construct a continuous normal field (through their cross-product) for shading and displacement mapping. Using this bifurcated representation, we are able to define an accurate proxy for Catmull-Clark surfaces that is efficient to evaluate on next-generation GPU architectures that expose a programmable tessellation unit.

Quad/Triangle Subdivision

In this paper we introduce a new subdivision operator that unifies triangular and quadrilateral subdivision schemes. Designers often want the added flexibility of having both quads and triangles in their models. It is also well known that triangle meshes generate poor limit surfaces when using a quad scheme, while quad‐only meshes behave poorly with triangular schemes. Our new scheme is a generalization of the well known Catmull‐Clark and Loop subdivision algorithms. We show that our surfaces are C 1 everywhere and provide a proof that it is impossible to construct such a C 2 scheme at the quad/triangle boundary. However, we provide rules that produce surfaces with bounded curvature at the regular quad/triangle boundary and provide optimal masks that minimize the curvature divergence elsewhere. We demonstrate the visual quality of our surfaces with several examples.

Real-time GPU rendering of piecewise algebraic surfaces

We consider the problem of real-time GPU rendering of algebraic surfaces defined by Bezier tetrahedra. These surfaces are rendered directly in terms of their polynomial representations, as opposed to a collection of approximating triangles, thereby eliminating tessellation artifacts and reducing memory usage. A key step in such algorithms is the computation of univariate polynomial coefficients at each pixel; real roots of this polynomial correspond to possibly visible points on the surface. Our approach leverages the strengths of GPU computation and is highly efficient. Furthermore, we compute these coefficients in Bernstein form to maximize the stability of root finding, and to provide shader instances with an early exit test based on the sign of these coefficients. Solving for roots is done using analytic techniques that map well to a SIMD architecture, but limits us to fourth order algebraic surfaces. The general framework could be extended to higher order with numerical root finding.

Approximating subdivision surfaces with Gregory patches for hardware tessellation

We present a new method for approximating subdivision surfaces with hardware accelerated parametric patches. Our method improves the memory bandwidth requirements for patch control points, translating into superior performance compared to existing methods. Our input is general, allowing for meshes that contain both quadrilateral and triangular faces in the input control mesh, as well as control meshes with boundary. We present two implementations of our scheme designed to run on Direct3D 11 class hardware equipped with a tessellator unit.

Fast Ray Sorting and Breadth-First Packet Traversal for GPU Ray Tracing

We present a novel approach to ray tracing execution on commodity graphics hardware using CUDA. We decompose a standard ray tracing algorithm into several data‐parallel stages that are mapped efficiently to the massively parallel architecture of modern GPUs. These stages include: ray sorting into coherent packets, creation of frustums for packets, breadth‐first frustum traversal through a bounding volume hierarchy for the scene, and localized ray‐primitive intersections. We utilize the well known parallel primitives scan and segmented scan in order to process irregular data structures, to remove the need for a stack, and to minimize branch divergence in all stages. Our ray sorting stage is based on applying hash values to individual rays, ray stream compression, sorting and decompression. Our breadth‐first BVH traversal is based on parallel frustum‐bounding box intersection tests and parallel scan per each BVH level.

Feature-adaptive GPU rendering of Catmull-Clark subdivision surfaces

We present a novel method for high-performance GPU-based rendering of Catmull-Clark subdivision surfaces. Unlike previous methods, our algorithm computes the true limit surface up to machine precision, and is capable of rendering surfaces that conform to the full RenderMan specification for Catmull-Clark surfaces. Specifically, our algorithm can accommodate base meshes consisting of arbitrary valence vertices and faces, and the surface can contain any number and arrangement of semisharp creases and hierarchically defined detail. We also present a variant of the algorithm which guarantees watertight positions and normals, meaning that even displaced surfaces can be rendered in a crack-free manner. Finally, we describe a view-dependent level-of-detail scheme which adapts to both the depth of subdivision and the patch tessellation density. Though considerably more general, the performance of our algorithm is comparable to the best approximating method, and is considerably faster than Stams exact method.

Estimating the Fundamental Matrix by Transforming Image Points in Projective Space

This paper proposes a novel technique for estimating the fundamental matrix by transforming the image points in projective space. We therefore only need to perform nonlinear optimization with one parameterization of the fundamental matrix, rather than considering 36 distinct parameterizations as in previous work. We also show how to preserve the characteristics of the data noise model from the original image space.

Holoportation: Virtual 3D Teleportation in Real-time

We present an end-to-end system for augmented and virtual reality telepresence, called Holoportation. Our system demonstrates high-quality, real-time 3D reconstructions of an entire space, including people, furniture and objects, using a set of new depth cameras. These 3D models can also be transmitted in real-time to remote users. This allows users wearing virtual or augmented reality displays to see, hear and interact with remote participants in 3D, almost as if they were present in the same physical space. From an audio-visual perspective, communicating and interacting with remote users edges closer to face-to-face communication. This paper describes the Holoportation technical system in full, its key interactive capabilities, the application scenarios it enables, and an initial qualitative study of using this new communication medium.