VectorAdam for Rotation Equivariant Geometry Optimization

The rise of geometric problems in machine learning has necessitated the development of equivariant methods, which preserve their output under the action of rotation or some other transformation. At the same time, the Adam optimization algorithm has proven remarkably effective across machine learning and even traditional tasks in geometric optimization. In this work, we observe that naively applying Adam to optimize vector-valued data is not rotation equivariant, due to per-coordinate moment updates, and in fact this leads to significant artifacts and biases in practice. We propose to resolve this deficiency with VectorAdam, a simple modification which makes Adam rotation-equivariant by accounting for the vector structure of optimization variables. We demonstrate this approach on problems in machine learning and traditional geometric optimization, showing that equivariant VectorAdam resolves the artifacts and biases of traditional Adam when applied to vector-valued data, with equivalent or even improved rates of convergence.

Roominoes: Generating Novel 3D Floor Plans From Existing 3D Rooms

Realistic 3D indoor scene datasets have enabled significant recent progress in computer vision, scene understanding, autonomous navigation, and 3D reconstruction. But the scale, diversity, and customizability of existing datasets is limited, and it is time-consuming and expensive to scan and annotate more. Fortunately, combinatorics is on our side: there are enough individual rooms in existing 3D scene datasets, if there was but a way to recombine them into new layouts. In this paper, we propose the task of generating novel 3D floor plans from existing 3D rooms. We identify three sub-tasks of this problem: generation of 2D layout, retrieval of compatible 3D rooms, and deformation of 3D rooms to fit the layout. We then discuss different strategies for solving the problem, and design two representative pipelines: one uses available 2D floor plans to guide selection and deformation of 3D rooms; the other learns to retrieve a set of compatible 3D rooms and combine them into novel layouts. We design a set of metrics that evaluate the generated results with respect to each of the three subtasks and show that different methods trade off performance on these subtasks. Finally, we survey downstream tasks that benefit from generated 3D scenes and discuss strategies in selecting the methods most appropriate for the demands of these tasks.

MatryODShka: Real-time 6DoF Video View Synthesis using Multi-Sphere Images

We introduce a method to convert stereo 360{\deg} (omnidirectional stereo) imagery into a layered, multi-sphere image representation for six degree-of-freedom (6DoF) rendering. Stereo 360{\deg} imagery can be captured from multi-camera systems for virtual reality (VR), but lacks motion parallax and correct-in-all-directions disparity cues. Together, these can quickly lead to VR sickness when viewing content. One solution is to try and generate a format suitable for 6DoF rendering, such as by estimating depth. However, this raises questions as to how to handle disoccluded regions in dynamic scenes. Our approach is to simultaneously learn depth and disocclusions via a multi-sphere image representation, which can be rendered with correct 6DoF disparity and motion parallax in VR. This significantly improves comfort for the viewer, and can be inferred and rendered in real time on modern GPU hardware. Together, these move towards making VR video a more comfortable immersive medium.