Shape matching plays an important role in various computer vision and graphics applications such as shape retrieval, object detection, image editing, image retrieval, etc. However, detecting shapes in cluttered images is still quite challenging due to the incomplete edges and changing perspective. In this paper, we propose a novel approach that can efficiently identify a queried shape in a cluttered image. The core idea is to acquire the transformation from the queried shape to the cluttered image by summarising all point-to-point transformations between the queried shape and the image. To do so, we adopt a point-based shape descriptor, the pyramid of arc-length descriptor (PAD), to identify point pairs between the queried shape and the image having similar local shapes. We further calculate the transformations between the identified point pairs based on PAD. Finally, we summarise all transformations in a 4D transformation histogram and search for the main cluster. Our method can handle both closed shapes and open curves, and is resistant to partial occlusions. Experiments show that our method can robustly detect shapes in images in the presence of partial occlusions, fragile edges, and cluttered backgrounds.

This paper tackles a challenging 2D collage generation problem, focusing on shapes: we aim to fill a given region by packing irregular and reasonably-sized shapes with minimized gaps and overlaps. To achieve this nontrivial problem, we first have to analyze the boundary of individual shapes and then couple the shapes with partially-matched boundary to reduce gaps and overlaps in the collages. Second, the search space in identifying a good coupling of shapes is highly enormous, since arranging a shape in a collage involves a position, an orientation, and a scale factor. Yet, this matching step needs to be performed for every single shape when we pack it into a collage. Existing shape descriptors are simply infeasible for computation in a reasonable amount of time. To overcome this, we present a brand new, scale- and rotation-invariant 2D shape descriptor, namely pyramid of arclength descriptor (PAD). Its formulation is locally supported, scalable, and yet simple to construct and compute. These properties make PAD efficient for performing the partial-shape matching. Hence, we can prune away most search space with simple calculation, and efficiently identify candidate shapes. We evaluate our method using a large variety of shapes with different types and contours. Convincing collage results in terms of visual quality and time performance are obtained.