Meschers: Geometry Processing of Impossible Objects

Impossible objects, geometric constructions that humans can perceive but that cannot exist in real life, have been a topic of intrigue in visual arts, perception, and graphics, yet no satisfying computer representation of such objects exists. Previous work embeds impossible objects in 3D, cutting them or twisting/bending them in the depth axis. Cutting an impossible object changes its local geometry at the cut, which can hamper downstream graphics applications, such as smoothing, while bending makes it difficult to relight the object. Both of these can invalidate geometry operations, such as distance computation. As an alternative, we introduce Meschers, meshes capable of representing impossible constructions akin to those found in M.C. Escher's woodcuts. Our representation has a theoretical foundation in discrete exterior calculus and supports the use-cases above, as we demonstrate in a number of example applications. Moreover, because we can do discrete geometry processing on our representation, we can inverse-render impossible objects. We also compare our representation to cut and bend representations of impossible objects.

Solving Vision Tasks with Simple Photoreceptors Instead of Cameras

A de facto standard in solving computer vision problems is to use a common high-resolution camera and choose its placement on an agent (i.e., position and orientation) based on human intuition. On the other hand, extremely simple and well-designed visual sensors found throughout nature allow many organisms to perform diverse, complex behaviors. In this work, motivated by these examples, we raise the following questions: 1. How effective simple visual sensors are in solving vision tasks? 2. What role does their design play in their effectiveness? We explore simple sensors with resolutions as low as one-by-one pixel, representing a single photoreceptor First, we demonstrate that just a few photoreceptors can be enough to solve many tasks, such as visual navigation and continuous control, reasonably well, with performance comparable to that of a high-resolution camera. Second, we show that the design of these simple visual sensors plays a crucial role in their ability to provide useful information and successfully solve these tasks. To find a well-performing design, we present a computational design optimization algorithm and evaluate its effectiveness across different tasks and domains, showing promising results. Finally, we perform a human survey to evaluate the effectiveness of intuitive designs devised manually by humans, showing that the computationally found design is among the best designs in most cases.