Abstract: Shape matching is a fundamental problem in computer vision and pattern recognition.For the problem of shape matching under projective transformations, we propose a novel shape descriptor based on the loop cross ratio, a novel projective invariant.We uniformly sample points on the convex hull of a planar shape.For each sample point, we obtain the intersections of the shape with the lines connecting the sample point and others and calculate the loop cross ratio spectrum using the intersections.Then, we measure the distance between two shapes by dynamic time warping algorithm with the nearest neighbor principle.The experiments demonstrate that the performance of the proposed method is better than the cross ratio spectrum and SIFT method on 13traffic signs with a wide range of affine transformations (208 images in total) and 32logos of television networks with a wide range of projective transformations (1 536 images in total), where some similar logos exist.