Research and Training in Vision and Computational Neuroscience

表面的视觉感知对于3D物体识别至关重要。自然场景中的所有表面都被赋予了纹理。在这个项目中，研究者开发了新的算法，从自然和合成场景的纹理中估计形状（表面的几何特征）。在微分拓扑的意义上，新的几何模型使用了带有附加结构的分段黎曼叶状。给定一个三维纹理表面，不一定是分段光滑的，可以构造一个叶状结构，其叶子形成一个二维纹理和分段光滑的数学表面的单参数族，近似给定对象。再加上在叶子上定义的目标函数，这样的2d纹理叶子是模拟世界上3d纹理表面的基本几何对象。我们可以使用算法从纹理中恢复分段光滑叶子的形状，例如曲率和倾斜。探索了几种基于场景的方法来构建纹理叶状，范围从解析（例如Hamilton-Jacobi方程）和拓扑技术（例如可积分布）到统计估计方法。为了测试理论和比较不同的算法，我们与神经科学实验家的同事一起进行了心理物理实验。特别是，目标函数可以根据心理物理数据进行数值近似。新模型应用于对称感知。研究了视觉皮层用于从纹理中估计形状的计算策略的建模问题，并与新的计算算法进行了比较。研究者概述了一个具体的培训计划，并与他在加州大学伯克利分校视觉和神经科学领域的资深同事进行研究合作，以实现该项目的认知和计算目标。我们怎么看？这个简单的问题没有简单的答案。视觉是一系列复杂的活动，从光线进入眼睛开始，到感知结束。人们能够准确地区分不同大小、对比度和颜色的物体。它们可以估计具有不同粗糙度和多种纹理的表面的曲率和方向，以及在短时间间隔内描述表面的属性，例如对称性和与其他熟悉物体的相似性。人类的视觉系统很容易胜过任何人造机器。几十年的视觉研究证明了以下方法的智慧：关键的见解通常来自于非常适合探索特定研究问题的模型。几何模型与计算技术的结合已经形成了现代生物和机器人视觉理论及其各种应用的基石。在这个项目中，首席研究员和他的同事们在纯数学中的高级几何理论（微分拓扑的叶理理论）与自然和合成环境中表面形状的视觉感知和估计之间建立了新的联系。在该理论的应用中，可以提到：在崎岖地形或难以到达的环境中无人驾驶车辆的机器人运动规划和导航；先进材料科学研究与设计中原子力显微镜材料图像的视觉形状估计对环境研究和生态学中易受弹道沉积和侵蚀的表面进行长期计算机检查；并对红外射电天文图像的大型数据库进行计算检查，以定位特定特征。正如人类视觉系统中的神经元并行执行任务一样，上述理论也适用于并行处理的实现。

Assadi 9707006 Visual perception of surfaces is crucial for 3D object recognition. All surfaces in natural scenes are endowed with texture. In this project, the investigator develops new algorithms to estimate shape (geometric characteristics of surfaces) from texture in natural and synthetic scenes. The new geometric models use piecewise Riemannian foliations, in the sense of differential topology, with additional structure. Given a 3D-textured surface, not necessarily piecewise smooth, one constructs a foliation whose leaves form a one-parameter family of 2D-textured and piecewise smooth mathematical surfaces approximating the given object. Together with an objective function defined on their leaves, such 2D-textured foliations are fundamental geometric objects that model 3D-textured surfaces in the world. One can use algorithms to recover shape from texture for the piecewise smooth leaves, e.g. curvature and slant. Several scene-based methods are explored to construct textured foliations, ranging from analytic (e.g. Hamilton-Jacobi equations) and topological techniques (e.g. integrable distributions) to statistical estimation methods. The psychophysical experiments to test the theory and compare different algorithms are explored with colleagues who are neuroscience experimentalists. In particular, the objective function can be numerically approximated based on psychophysical data. The new models are applied to perception of symmetry. The problem of modeling computational strategies employed by the visual cortex to estimate shape from texture, and their comparison with the new computational algorithms, is pursues. The investigator outlines a concrete training program and research collaboration with his senior colleagues in vision and neuroscience at UC Berkeley in order to achieve the cognitive and computational objectives of the project. How do we see? This simple question does not have a simple answer. Vision is a complex series of eve nts that begins when light enters the eyes and ends with perception. People are able to discriminate between objects of different size, contrast and color with precision. They can estimate curvature and orientation of surfaces with varying roughness and multitudes of texture, as well as describe within short time intervals properties of surfaces such as symmetry and similarity to other familiar objects. The human visual system easily outperforms any man-made machine. Decades of research in vision demonstrate the wisdom of the following approach: Key insights generally come from models that are well-suited for exploring a specific research question. Geometric models coupled with computational techniques have formed a cornerstone of modern theories of biological as well as robot vision, and of their diverse applications. In this project, the principal investigator and his colleagues establish a new link between advanced geometric theories in pure mathematics (theory of foliations from differential topology) and visual perception and estimation of shape of surfaces in natural and synthetic environments. Among applications of the theory, one could mention: robot motion planning and navigation of manless vehicles in rough terrain or unreachable environments; visual shape estimation of images of materials obtained by atomic force microscopy in scientific research and design of advanced materials; long-term computerized inspection of surfaces subject to ballistic deposition and erosion in environmental studies and ecology; and computational inspection of large databases of images from infrared radio astronomy in order to locate specific features. Just as the neurons in human visual system perform their tasks in parallel, the above-mentioned theory lends itself to parallel processing implementation.