We study inferring a tree-structured representation from a single image for object shading. Prior work typically uses the parametric or measured representation to model shading, which is neither interpretable nor easily editable. We propose using the shade tree representation, which combines basic shading nodes and compositing methods to factorize object surface shading. The shade tree representation enables novice users who are unfamiliar with the physical shading process to edit object shading in an efficient and intuitive manner. A main challenge in inferring the shade tree is that the inference problem involves both the discrete tree structure and the continuous parameters of the tree nodes. We propose a hybrid approach to address this issue. We introduce an auto-regressive inference model to generate a rough estimation of the tree structure and node parameters, and then we fine-tune the inferred shade tree through an optimization algorithm. We show experiments on synthetic images, captured reflectance, real images, and non-realistic vector drawings, allowing downstream applications such as material editing, vectorized shading, and relighting. Project website: https://chen-geng.com/inv-shade-trees.

Motion graphics videos are widely used in Web design, digital advertising, animated logos and film title sequences, to capture a viewer's attention. But editing such video is challenging because the video provides a low-level sequence of pixels and frames rather than higher-level structure such as the objects in the video with their corresponding motions and occlusions. We present a motion vectorization pipeline for converting motion graphics video into an SVG motion program that provides such structure. The resulting SVG program can be rendered using any SVG renderer (e.g. most Web browsers) and edited using any SVG editor. We also introduce a program transformation API that facilitates editing of a SVG motion program to create variations that adjust the timing, motions and/or appearances of objects. We show how the API can be used to create a variety of effects including retiming object motion to match a music beat, adding motion textures to objects, and collision preserving appearance changes.

We consider dimensionality reduction for data sets with two or more independent degrees of freedom. For example, measurements of deformable shapes with several parts that move independently fall under this characterization. Mathematically, if the space of each continuous independent motion is a manifold, then their combination forms a product manifold. In this paper, we present an algorithm for manifold factorization given a sample of points from the product manifold. Our algorithm is based on spectral graph methods for manifold learning and the separability of the Laplacian operator on product spaces. Recovering the factors of a manifold yields meaningful lower-dimensional representations, allowing one to focus on particular aspects of the data space while ignoring others. We demonstrate the potential use of our method for an important and challenging problem in structural biology: mapping the motions of proteins and other large molecules using cryo-electron microscopy data sets.