Uniqueness in Shape from Shading Revisited

We analyse the problem of representing solutions of first-orderpartial differential equations in terms of complete integrals and envelopes. In this context, we revisit the uniqueness results alreadyexisting in the shape-from-shading literature that concern eikonalequations corresponding to the images of a Lambertian hemi-sphere and aLambertian plane. We show that the approach adopted by Brooks in [2, 3] isincomplete and subsequently re-establish its uniqueness claims.     

利用等值线跟踪的快速步进法

针对由明暗重构三维形状及普遍意义上的Eikonal偏微分方程求解问题，提出一种基于等值线跟踪的快速步进法，通过跟踪等值线的传播，利用迎风格式对等值线附近的扩展区域进行单遍或两遍更新，使求解过程具有O（N）复杂度．实验结果表明，该方法改进了已有快速步进法的速度和精度，可有效地处理多源问题及由明暗重构形状问题，且在复杂情形下速度优于快速扫描法．     

真实感3D人脸快速建模研究*

现有的三维人脸建模方法存在三点不足：建模条件苛刻、建模精度不高和建模时间长。针对以上不足,提出明暗恢复形状（SFS）和局部形变模型融合的3D人脸建模方法。该方法利用SFS快速恢复3D人脸粗糙数据,得到3D轮廓脸;然后分别对人脸不同局部应用形变模型恢复其局部3D精确数据,并使用其对轮廓脸进行内插平滑处理重建出高精度3D人脸模型。实验结果表明：该方法能够获得较好的建模精度,在短时间内可以通过单幅真实图像重建出个性化的三维人脸模型。     

Symmetric Shape-from-Shading Using Self-ratio Image

In this paper, we present a symmetric shape-from-shading (SFS) approach to recover both shape and albedo for symmetric objects. Lambertian surfaces with unknown varying albedo and orthographic projections are assumed. In our formulation of symmetric SFS, we have two image irradiance equations. One is the standard equation used in SFS, and the other is a self-ratio image irradiance equation. This new image irradiance equation relates the self-ratio image which is defined as the ratio of two-halves of the input image to light source and surface shape. The introduction of the self-ratio image facilitates the direct use of symmetry cue. Based on the self-ratio image, a new model-based symmetric source-from-shading algorithm is also presented. We then propose symmetric SFS algorithms to recover both shape and albedo from a single image and present experimental results.The new symmetric SFS scheme has one important property: the existence of a unique (global) solution which consists of unique (local) solutions at each point simultaneously obtained using the intensity information at that point and the surrounding local region and the assumption of a C ² surface. Proofs for the existence of a unique solution in the cases of unknown constant and non-constant albedos are provided.     

Recognition of Curvature Radius in Robot Moving in Bent Pipe

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基于镜面高光检测的明暗恢复形状新方法

镜面高光是由明暗恢复形状算法的重大障碍,但是对于单幅灰度图像,因为只包含亮度信息,现有以色度分析和极化分析为基础的高光检测方法均不能适用.为此,提出了一种利用表面形态分布信息检测镜面高光的方法.该方法充分利用成像过程信息,通过对表面法向量的估计,采用模拟退火算法,计算各反射成分的最大后验概率,从而实现高光区域检测,最后,利用基于曲率连续性假设的约束补色方法移除镜面高光.实验结果表明提出的算法在仿真和真实图像的高光检测中均具有较好的检测效果,有效提高了含镜面高光图像的表面恢复精度.     

基于曲面法向量的曲面恢复

从另一个角度研究三维曲面的恢复,即根据曲面法向量,考虑多块曲面的重构.算法输入的数据是估计的曲面法向量,比如输入的数据是根据从阴影恢复形状或从纹理恢复形状等计算机视觉低层次处理中得到.通过球面坐标变换把曲面法向量分解成两个函数;然后再对这两个函数进行滤波处理,通过对这两个分割的叠加将空间曲面分割成几个子曲面;最后利用Green函数分别恢复各个子曲面.虽然只利用了一般的图像处理技术,却能得到比传统的基于曲面法向量的方法更好的结果,特别是边界部分的恢复.这是因为传统的方法只是考虑恢复一个曲面模型,因此在不同曲面的边界上会产生模糊.最后利用模拟数据和由阴影恢复形状算法获取真实数据来评价提出的算法,并都与传统的方法进行了比较.     

Shape-from-Shading Under Perspective Projection

Shape-from-Shading (SfS) is a fundamental problem in Computer Vision. A very common assumption in this field is that image projection is orthographic. This paper re-examines the basis of SfS, the image irradiance equation, under a perspective projection assumption. The resultant equation does not depend on the depth function directly, but rather, on its natural logarithm. As such, it is invariant to scale changes of the depth function. A reconstruction method based on the perspective formula is then suggested; it is a modification of the Fast Marching method of Kimmel and Sethian. Following that, a comparison of the orthographic Fast Marching, perspective Fast Marching and the perspective algorithm of Prados and Faugeras on synthetic images is presented. The two perspective methods show better reconstruction results than the orthographic. The algorithm of Prados and Faugeras equates with the perspective Fast Marching. Following that, a comparison of the orthographic and perspective versions of the Fast Marching method on endoscopic images is introduced. The perspective algorithm outperformed the orthographic one. These findings suggest that the more realistic set of assumptions of perspective SfS improves reconstruction significantly with respect to orthographic SfS. The findings also provide evidence that perspective SfS can be used for real-life applications in fields such as endoscopy.This research has been supported in part by Tel-Aviv University fund, the Adams Super-Center for Brain Studies, the Israeli Ministry of Science, the ISF Center for Excellence in Applied Geometry, the Minerva Center for geometry, and the A.M.N. fund.     

Improved Diffuse Reflection Models for Computer Vision

There are many computational vision techniques that fundamentally rely upon assumptions about the nature of diffuse reflection from object surfaces consisting of commonly occurring nonmetallic materials. Probably the most prevalent assumption made about diffuse reflection by computer vision researchers is that its reflected radiance distribution is described by the Lambertian model, whether the surface is rough or smooth. While computationally and mathematically a relatively simple model, in physical reality the Lambertian model is deficient in accurately describing the reflected radiance distribution for both rough and smooth nonmetallic surfaces. Recently, in computer vision diffuse reflectance models have been proposed separately for rough, and, smooth nonconducting dielectric surfaces each of these models accurately predicting salient non-Lambertian phenomena that have important bearing on computer vision methods relying upon assumptions about diffuse reflection. Together these reflectance models are complementary in their respective applicability to rough and smooth surfaces. A unified treatment is presented here detailing important deviations from Lambertian behavior for both rough and smooth surfaces. Some speculation is given as to how these separate diffuse reflectance models may be combined.     

Shape Reconstruction of 3D Bilaterally Symmetric Surfaces

The paper presents a new approach for shape recovery based on integrating geometric and photometric information. We consider 3D bilaterally symmetric objects, that is, objects which are symmetric with respect to a plane (e.g., faces), and their reconstruction from a single image. Both the viewpoint and the illumination are not necessarily frontal. Furthermore, no correspondence between symmetric points is required.The basic idea is that an image taken from a general, non frontal viewpoint, under non-frontal illumination can be regarded as a pair of images. Each image of the pair is one half of the object, taken from different viewing positions and with different lighting directions. Thus, one-image-variants of geometric stereo and of photometric stereo can be used. Unlike the separate invocation of these approaches, which require point correspondence between the two images, we show that integrating the photometric and geometric information suffice to yield a dense correspondence between pairs of symmetric points, and as a result, a dense shape recovery of the object. Furthermore, the unknown lighting and viewing parameters, are also recovered in this process.Unknown distant point light source, Lambertian surfaces, unknown constant albedo, and weak perspective projection are assumed. The method has been implemented and tested experimentally on simulated and real data.