Ambiguous Shape from Shading with Critical Points

The eikonal equation can have an infinite number of solutions when the image has critical points. We exhibit a family, indexed by a continuous parameter, of non isomorphic surfaces with one critical point, which give the same simple image. Hence, shape from shading can be an ill-posed problem when no additional condition on the shape is imposed, even when the image has critical points. Also, deformations without distortion are possible, i.e., there can exist a continuous deformation of the surface which does not modify its image.     

正则化方法在线性SFS问题中的应用

线性ShapefromShading问题(LSFS)是一类特殊的ShapefromShading问题,此时反射图是表面梯度分量的线性组合的函数。文章在待恢复表面平滑和已知光照方向等假定下,把线性SFS问题正则化,并利用Kaczmarz算法求解得到线性方程组。此种方法能处理区域形状不规则和边界条件不完备的情况。文章用Kaczmarz算法给出了一种从不可积向量场求得最接近的可积向量场的方法,该方法能处理区域形状不规则的情况。     

Application of Self-Organisation Neural Network for Direct Shape from Shading

In this paper, a supervised self-organisation Neural Network (NN) for direct shape from shading is developed. The structure of the NN for the inclined light source model is derived based on the maximum uphill direct shape from shading approach. The major advantage of the NN model presented is the parallel learning or weight evolution for the direct shading. Here the proved convergent learning rule, the rate of convergence and a zero initialisation condition are shown. To increase the rate of convergence, the momentum factor is introduced. Further-more, the application of the network on IC (Integrated Circuit) component shape reconstruction is presented.     

用单幅图像重建三维凸面和两类鞍面的方法

利用Eikonal方程的粘性解给出了基于单幅图像的凸面三维重建算法;定义了2类鞍面——加性鞍面和乘性鞍面．利用凸面法和凹面法从鞍面单幅图像重建2个抛物柱面,然后根据鞍面的结构特点将2个抛物柱面重新合成鞍面．文中算法从临界点开始计算,不要求边界条件,具有较高的精确度．最后通过实验分析了该算法对噪声的敏感性．     

基于混合反射模型的SFS有限元方法的研究

提出了基于混合反射模型的由明暗恢复物体三维形状的有限元算法。用正方形面元逼近光滑曲面,把曲面表示为所有节点基函数的线性组合;基于既含有漫反射成分又有镜面反射成分的混合模型,结合节点基函数,将反射图线性化。考虑数字图像的特点,直接使用离散形式的SFS问题的亮度约束形式,用最小化方法得到高度满足的线性方程;使用Kaczmarz算法计算出表面三维形状。使用合成图像和实际图像验证该文算法的有效性,探讨了该算法的性能。     

Can the Sun's Direction be Estimated from an Image Prior to the Computation of Object Shape?

Various computational techniques have been developed that performreasonably well in inferring shape from shading. However, thesetechniques typically require substantial prerequisite information ifthey are to evolve an estimate of surface shape. It is thereforeinteresting to consider how depth might be inferred from shadinginformation without prior knowledge of various scene conditions. Oneapproach has been to undertake a pre-processing step ofestimating the light-source direction, thereby providing input tothe computation of shape from shading. In this paper, we presentevidence that a versatile light-source-direction estimator isunattainable, and propose that, in the absence of domain-specificknowledge, shape and light-source direction should be determined ina coupled manner     

An optimal control model for a system of degenerate parabolic integro-differential equations

An initial-boundary-value problem for a system of degenerate parabolic integro-differential equations is considered. The sufficient conditions for the existence and uniqueness of its generalized solution and for the existence of at least one optimal control for a given performance functional are obtained. A stable numerical solution to the initial-boundary-value problem is derived for a locally one-dimensional case and conditions are formulated for constructing a stable numerical algorithm of the optimal control problem on a class of piecewise-smooth control functions. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 90–102, November–December 2007.     

Necessary and sufficient conditions of existence and uniqueness of solutions to integral equations of actuarial mathematics

Necessary and sufficient conditions of existence and uniqueness of solutions of integral equations are established for ruin probability as a function of the initial capital of an insurance company. Several sufficient conditions and correctness conditions of the problem of finding ruin probability are also established. A general method of successive approximations for solution of this problem is substantiated. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 157–164, September–October 2006.