Recognizing planar objects such as characters, symbols and logos is considered a hard problem in computer vision due to the possibility of these shapes suffer from different kinds of disturbances: projective or other nonlinear deformations, occlusions and spurious insertions. Different planar descriptors have been proposed by taking advantage of geometric features that are invariant to certain image transformations, usually linear ones such as scaling, rotation and affinity. In this work, a new descriptor of planar shapes robust to projective deformations is proposed: Cross Ratio Arrays (CRA). The descriptor is based on tracing rays across the images and collecting their intersections with the borders of the shapes to assemble arrays of computed cross ratios, one of the most fundamental projective invariants. Higher level arrays are built out of these sets of arrays from both query and template shapes, which ultimately allows us to identify correspondences in these shapes to estimate how projectively deformed one shape is from the other. Experiments with synthetic shapes as well as real world scene shapes suffering from severe projective deformations were conducted, with CRA outperforming state-of-the-art descriptors. In addition, tests were performed with different levels of occlusion and weak nonlinear deformations to evidence CRA’s robustness to such cases.

识别诸如字符、符号和徽标之类的平面对象被认为是计算机视觉中的一个难题，因为这些形状可能会受到不同类型的干扰：投影或其他非线性变形、遮挡和虚假插入。已经通过利用对某些图像变换不变的几何特征提出了不同的平面描述符，通常是线性变换，例如缩放、旋转和亲和力。在这项工作中，提出了一种对投影变形鲁棒的平面形状的新描述符：交叉比阵列（CRA）。该描述符基于在图像上跟踪光线并收集它们与形状边界的交点以组装计算出的交叉比数组，这是最基本的射影不变量之一。更高级别的数组由来自查询和模板形状的这些数组集构建而成，这最终使我们能够识别这些形状中的对应关系，以估计一个形状与另一个形状的投影变形程度。对合成形状以及遭受严重投影变形的现实世界场景形状进行了实验，CRA 的表现优于最先进的描述符。此外，还对不同级别的咬合和弱非线性变形进行了测试，以证明 CRA 对此类情况的鲁棒性。对合成形状以及遭受严重投影变形的现实世界场景形状进行了实验，CRA 的表现优于最先进的描述符。此外，还对不同级别的咬合和弱非线性变形进行了测试，以证明 CRA 对此类情况的鲁棒性。对合成形状以及遭受严重投影变形的现实世界场景形状进行了实验，CRA 的表现优于最先进的描述符。此外，还对不同级别的咬合和弱非线性变形进行了测试，以证明 CRA 对此类情况的鲁棒性。