Abstract
We exploit a key result from visual psychophysics---that individuals perceive shape qualitatively---to develop the use of a geometrical/topological "invariant'' (the Morse--Smale complex) relating image structure with surface structure. Differences across individuals are minimal near certain configurations such as ridges and boundaries, and it is these configurations that are often represented in line drawings. In particular, we introduce a method for inferring a qualitative three-dimensional shape from shading patterns that link the shape-from-shading inference with shape-from-contour inference. For a given shape, certain shading patches approach "line drawings'' in a well-defined limit. Under this limit, and invariably with respect to rendering choices, these shading patterns provide a qualitative description of the surface. We further show that, under this model, the contours partition the surface into meaningful parts using the Morse--Smale complex. These critical contours are the (perceptually) stable parts of this complex and are invariant over a wide class of rendering models. Intuitively, our main result shows that critical contours partition smooth surfaces into bumps and valleys, in effect providing a scaffold on the image from which a full surface can be interpolated.
Abstract (translated)
我们利用视觉心理物理学的关键结果 - 个体定性地感知形状 - 开发使用几何/拓扑“不变”（莫尔斯 - 斯马尔复合体）将图像结构与表面结构相关联。在某些配置（例如脊和边界）附近是最小的，并且这些配置通常在线条图中表示。特别地，我们引入了一种方法，用于从连接阴影形状的阴影图案推断出定性的三维形状。从轮廓推断的形状推断。对于给定的形状，某些着色补丁在明确定义的极限中接近“线条图”。在这个限制下，并且总是在渲染选择方面，这些阴影图案提供了表面的定性描述。我们进一步表明，在这个模型下，轮廓使用Morse - Smale复合体将表面划分为有意义的部分。这些关键轮廓是这个复合体的（感知上）稳定的部分，并且在一大类渲染模型中是不变的。直观地，我们的主要结果表明，临界轮廓将光滑表面划分为凸起和凹陷，实际上在图像上提供了可以插入整个表面的支架。
URL
https://arxiv.org/abs/1705.07329
