We propose a generalized equation to represent a continuum of surface reconstruction solutions of a given non-integrable gradient field. We show that common approaches such as Poisson solver and Frankot-Chellappa algorithm are special cases of this generalized equation. For a N x N pixel grid, the subspace of all integrable gradient fields is of dimension N 2 - 1. Our framework can be applied to derive a range of meaningful surface reconstructions from this high dimensional space. The key observation is that the range of solutions is related to the degree of anisotropy in applying weights to the gradients in the integration process. While common approaches use isotropic weights, we show that by using a progression of spatially varying anisotropic weights, we can achieve significant improvement in reconstructions. We propose (a) α-surfaces using binary weights, where the parameter a allows trade off between smoothness and robustness, (b) M-estimators and edge preserving regularization using continuous weights and (c) Diffusion using affine transformation of gradients. We provide results on photometric stereo, compare with previous approaches and show that anisotropic treatment discounts noise while recovering salient features in reconstructions.

What Is the Range of Surface Reconstructions from a Gradient Field

Realistic hair modeling is a fundamental part of creating virtual humans in computer graphics. This paper surveys the state of the art in the major topics of hair modeling: hairstyling, hair simulation, and hair rendering. Because of the difficult, often unsolved problems that arise in alt these areas, a broad diversity of approaches is used, each with strengths that make it appropriate for particular applications. We discuss each of these major topics in turn, presenting the unique challenges facing each area and describing solutions that have been presented over the years to handle these complex issues. Finally, we outline some of the remaining computational challenges in hair modeling

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A Survey on Hair Modeling: Styling, Simulation, and Rendering

While total variation is among the most popular regularizers for variational problems, its extension to functions with values in a manifold is an open problem. In this paper, we propose the first algorithm to solve such problems which applies to arbitrary Riemannian manifolds. The key idea is to reformulate the variational problem as a multilabel optimization problem with an infinite number of labels. This leads to a hard optimization problem which can be approximately solved using convex relaxation techniques. The framework can be easily adapted to different manifolds including spheres and three-dimensional rotations, and allows to obtain accurate solutions even with a relatively coarse discretization. With numerous examples we demonstrate that the proposed framework can be applied to variational models that incorporate chromaticity values, normal fields, or camera trajectories.

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Total Variation Regularization for Functions with Values in a Manifold

Dynamic hair strands have complex structures and experience intricate collisions and occlusion, posing significant challenges for high-quality reconstruction of their motions. We present a comprehensive dynamic hair capture system for reconstructing realistic hair motions from multiple synchronized video sequences. To recover hair strands' temporal correspondence, we propose a motion-path analysis algorithm that can robustly track local hair motions in input videos. To ensure the spatial and temporal coherence of the dynamic capture, we formulate the global hair reconstruction as a spacetime optimization problem solved iteratively. Demonstrated using a range of real-world hairstyles driven by different wind conditions and head motions, our approach is able to reconstruct complex hair dynamics matching closely with video recordings both in terms of geometry and motion details.

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Dynamic hair capture using spacetime optimization

多角形的模型是 3D 目标的受欢迎的代表。在计算应用的多角形的模型的使用经常要求一个模型到适当地绑 3D 固体。也就是说，多角形的模型需要被闭上，歧管，并且没有自我交叉。这篇论文为修理不满足的模型调查可观的文学这标准，集中于由他们的方法论和能力分类他们。我们希望把指针提供给进一步的读物因为研究人员和专业人员，和为未来的有希望的方向的建议研究努力。这篇文章(doi:10.1007/s11390-009-9206-7 ) 的联机版本包含增补材料，它对授权的用户可得到。

Fixing Geometric Errors on Polygonal Models： A Survey

This paper describes a new hybrid technique for cartoon hair animation, one that allows the animators to create attractive and controllable hair animations without having to draw everything by hand except a sparse set of key frames. We demonstrate how to give a cel animation character accentuated hair motion. The novelty of this approach is that we neither simply interpolate the key frames nor generate the movement of the hair only using physical simulations. From a small number of rough sketches we prepare key frames that are used as indicators of hair motion. The hair movements are created based on a hair motion database built from physical simulations custom-designed by the animator. Hair animations with constraints from the key frames can be generated in two stages: a matching process to search for the desired motion sequences from the database and then smoothly connect them; the discrepancies between the database sequences and the key frames are interpolated throughoutthe animation using transition function.

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Simulation-based cartoon hair animation

In this paper, we present a surface reconstruction via 2D strokes and a vector field on the strokes based on a two-step method. In the first step, from sparse strokes drawn by artists and a given vector field on the strokes, we propose a nonlinear vector interpolation combining total variation (TV) and H 1 regularization with a curl-free con- straint for obtaining a dense vector field. In the second step, a height map is obtained by integrating the dense vector field in the first step. Jump discontinuities in surface and discontinuities of surface gradients can be well reconstructed without any surface distortion. We also provide a fast and efficient algorithm for solving the proposed func- tionals. Since vectors on the strokes are interpreted as a projection of surface gradients onto the plane, different types of strokes are easily devised to generate geometrically crucial structures such as ridge, valley, jump, bump, and dip on the surface. The stroke types help users to create a surface which they intuitively imagine from 2D strokes. We compare our results with conventional methods via many examples. AMS subject classifications: 65K10, 65D18, 65D17

Stroke-Based Surface Reconstruction

Processes such as modeling, rendering and simulating hair are essential for creating virtual humans in various CG applications. CG hair motion simulations are commonly constructed using a physics-based model and have been extensively researched. While physics-based approaches have achieved effective and sophisticated hair motion, data-driven approaches for hair motion have been scarcely researched. This paper therefore outlines our hair animation approach which uses Motion Capture System to capture 3D hair motion. Our approach enables users to easily simulate complex hair motions such as the collision between hair strands and the human body and the movement of hair strands as they are blown in a variety of directions by wind.

Hair motion reconstruction using motion capture system

The role of shadow is important in cartoon animation. Shadows in hand-drawn animation reflect the expression of the animators' style, rather than mere physical phenomena. However shadows in 3DCG cannot express such an animators' touch. In this paper we propose a novel method for editing the shadow with both advantages of hand drawn animation and 3DCG technology. In particular, we discuss two phases that enable animators to transform and deform the shadow tweakably. The first phase is that a shadow projection matrix is applied to deform the shape of the shadow. The second one is that we manipulate vectors to transform the shadow such as scaling and translation. These vectors are used in shadow volume method. The shadows are edited directably by integration of these two phases. Our approach enables animators to edit the shadow by simple mouse operations. As a result, the animators can not only produce shadows automatically but also reflect their style easily. Once the shape and location of shadow are decided by animators' style in our method, 3DCG techniques can produce consistent shadow in object motion interactively.

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Tweakable Shadows for Cartoon Animation

This paper describes a new approach to create cartoon hair animation that allows users to use existing cel character animation sequences. We demonstrate the generation of cartoon hair animation accentuated in ‘anime-like’ motions. The novelty of this method is that users can choose the existing cel animation of a character's hair animation and apply environmental elements such as wind to other characters with a three-dimensional structure. In fact, users can reuse existing cartoon sequences as input to endow another character with environmental elements as if both characters exist in the same scene. A three-dimensional character's hair motions are created based on hair motions from input cartoon animation sequences. First, users extract hair shapes at each frame from input sequences from which they then construct physical equations. ‘Anime-like’ hair motion is created by using these physical equations. Copyright © 2006 John Wiley & Sons, Ltd.

Eiji Sugisaki

Papers

Simulation-based cartoon hair animation

Stroke-Based Surface Reconstruction

Hair motion reconstruction using motion capture system

Tweakable Shadows for Cartoon Animation

Hair motion cloning from cartoon animation sequences