Image Algebra and Automatic Shape Recognition
Image Algebra and Automatic Shape Recognition
复制标题
图像代数和自动形状识别
DOI：
10.1109/taes.1985.310539
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发表时间：
1985
影响因子：
4.4
通讯作者：
W. Brown
中科院分区：
文献类型：
--
作者：
T. Crimmins;W. Brown
形状识别可以通过集合论运算来进行。除了通常的并集、补集等集合论运算外，还加入了两个集合（或图像）之间的侵蚀运算。然后表明，集合之间的这些运算可作为所有通常非线性的平移不变变换（即与平移交换的变换）的表示定理的基础。通过将图像和形状视为 n 维笛卡尔空间中的点集（对于二值图像，n = 2，对于灰度图像，n = 3，对于包含颜色、偏振等的图像，n = 3），形状或模式识别问题转换为检测图像中特定集合的出现的问题。这个问题与侵蚀的运行密切相关。通过引入补图像和补形状，找到了一种用于自动形状识别的通用计算机，为表示定理和相关结果提供了建设性的证明。
Shape recognition can be carried out with set theory operations. In addition to the usual set theory operations of union, complement, etc., the operation of erosion between two sets (or images) is incorporated. Then it is shown that these operations between sets serve as a basis for representation theorems for all, generally nonlinear, translation invariant transformations, (i.e., transformations which commute with translations). By treating images and shapes as point sets in n-dimensional Cartesian space (n = 2 for binary images, n = 3 for gray scale images, and larger n for images that incorporate color, polarization, and the like), the problem of shape or pattern recognition is converted to the problem of detecting the occurrences of specific sets within an image. This problem is closely related to the operation of erosion. By introducing complement images and complement shapes, a generic computer for automatic shape recognition is found which provides a constructive proof of the representation theorem and related results.