Object detection can be formulated as a point matching problem when objects are modeled by point sets. Moments, which have been widely used for point matching, are limited to affine transformations as their support point sets cannot keep invariant. To address this problem, we developed an affine invariant centroid tree (AICT) to obtain a rigorous affine invariant support point set (SPS). The algorithm is constructed by a recursive process: the point set is first divided by the vector from the certain point to the centroid of the point set, and the centroids of subsets are used to generate vectors for renewed partitions. In addition, the centroids of the subsets are stored to form an AICT. The AICT represents the inherent structure of the point set. It is highly tolerant to noise and outliers due to the partitions on the whole point set. More importantly, it is affine invariant owing to the affine invariance of partition. Therefore, we can get rigorous affine invariant descriptors while moments are combined with AICT. The experimental results on synthesized and real data verify that our proposed algorithm outperforms the state-of-the-art point matching methods including shape context, iterative closet point, and the method adopting thin plate spline for rigid robust point matching (TPS-RPM).

当对象由点集建模时，对象检测可以表述为点匹配问题。已广泛用于点匹配的矩仅限于仿射变换，因为它们的支持点集不能保持不变。为了解决这个问题，我们开发了仿射不变质心树（AICT）来获得严格的仿射不变支持点集（SPS）。该算法是通过递归过程构造的：首先将点集除以从某个点到点集质心的向量，并使用子集的质心生成向量用于重新划分。此外，存储子集的质心以形成 AICT。AICT 表示点集的固有结构。由于整个点集上的分区，它对噪声和异常值具有很高的容忍度。更重要的是，由于分区的仿射不变性，它是仿射不变的。因此，我们可以得到严格的仿射不变描述符，而矩与 AICT 相结合。在合成数据和真实数据上的实验结果证明，我们提出的算法优于最先进的点匹配方法，包括形状上下文、迭代最近点和采用薄板样条的刚性鲁棒点匹配方法 (TPS-RPM) .