Mathematical Sciences: Mathematical and Computational Problems in Object Recognition

该研究计划侧重于对象识别的数学方面。有两类问题。首先是在场景中以任意旋转、位置和比例定位的刚性物体的识别。假设事先已知大量的形状，那么问题是设计出计算效率高的算法来识别给定场景中存在的这些物体。将探索顺序和自适应策略，其中进行一系列基于图像的观测，并根据先前观测的结果选择观测。这与编码理论、实验顺序设计、多臂强盗问题、“二十问”游戏，当然还有之前在机器视觉方面的工作有着密切的联系。第二类问题是对非刚性或可变形物体的识别。例子包括手写数字和各种生物形状，如叶子、手、细胞器等。在这里，形状建模的问题似乎是中心。提出了一种基于可变形模板的方法。模板是捕获全局特征的原型，而变形是满足某些规则约束的随机转换，它作用于模板以产生对象的可能表示。所提出的形状模型提出了一定的识别算法，这些将在各种应用领域进行探索。

The research program focuses on mathematical aspects of object recognition. There are two classes of problems. The first is the recognition of rigid objects positioned in a scene at arbitrary rotations, locations, and scales. A large repertoire of shapes is assumed known in advance, and the problem is to then devise computationally efficient algorithms for recognizing which, if any, of these objects are present in a given scene. Sequential and adaptive strategies will be explored, in which a sequence of image-based observations is made, with the choice of an observation depending upon the results of previous observations. There are close connections to coding theory, sequential design of experiments, multi-armed bandit problems, the game of "twenty questions," and, of course, previous work in machine vision. The second class of problems is the recognition of nonrigid, or deformable, objects. Examples include handwritten numerals and various biological shapes, such as leaves, hands, organelles, etc. Here the issue of shape modeling appears to be central. An approach through deformable templates is proposed. Templates are prototypes which capture global characteristics, whereas deformations are random transformations, satisfying certain regularity constraints, that act upon templates to produce the possible presentations of an object. The proposed shape models suggest certain recognition algorithms, and these will be explored in a variety of application areas.