Shallow Signed Distance Functions for Kinematic Collision Bodies

TL;DR

This work designs a learning-based representation of SDFs for human avatars whoes bodies change shape kinematically due to joint-based skinning that is extremely fast and accurate and demonstrates its applicability with real-time simulation of garments driven by animated characters.

Abstract

We present learning-based implicit shape representations designed for real-time avatar collision queries arising in the simulation of clothing. Signed distance functions (SDFs) have been used for such queries for many years due to their computational efficiency. Recently deep neural networks have been used for implicit shape representations (DeepSDFs) due to their ability to represent multiple shapes with modest memory requirements compared to traditional representations over dense grids. However, the computational expense of DeepSDFs prevents their use in real-time clothing simulation applications. We design a learning-based representation of SDFs for human avatars whoes bodies change shape kinematically due to joint-based skinning. Rather than using a single DeepSDF for the entire avatar, we use a collection of extremely computationally efficient (shallow) neural networks that represent localized deformations arising from changes in body shape induced by the variation of a single joint. This requires a stitching process to combine each shallow SDF in the collection together into one SDF representing the signed closest distance to the boundary of the entire body. To achieve this we augment each shallow SDF with an additional output that resolves whether or not the individual shallow SDF value is referring to a closest point on the boundary of the body, or to a point on the interior of the body (but on the boundary of the individual shallow SDF). Our model is extremely fast and accurate and we demonstrate its applicability with real-time simulation of garments driven by animated characters.

Figures (9)

• Figure 1: Example of combinining two SSDFs into one. The rectange $ABCD$ is divided into two parts $AEFD$ and $BHGC$. (a) Point $X$ is closer to the interior boundary than the true boundary for both SSDFs. (b) Red regions $JFE$ and $HIG$ shows incorrect boundary information for $AEFD$ and $BHGC$. The two partitions above lead to undesired regions where the correct SDF cannot be computed. (c) Our partition is analogous to AEFD and BHGC here so that the incorrect boundary regions (red) do not intersect, therefore SDF can be computed for all interior points.
• Figure 2: Model Architecture. Weights $\{\mathbf{W}^{n}_{ij}\}$ and biases $\{b^{n}_{ij}\}$ between the $n^{th}$ and $(n+1)^{th}$ layers for channel $l$ are computed as in Equation \ref{['eq:weights']}. The figure illustrates the architecture for $N_J=5$ (3 hidden layers) and each hidden layer has $n=8$ activation nodes. The hidden layers have rectified linear unit (ReLU) activation function, the output layer has linear activation function. This illustration assumes the joint has $D_i=3$ degrees of freedom: The rotation angles in $X,Y,Z$ direction.
• Figure 3: The canonical space of SSDF for the joint knee is determined by thigh, the parent of knee in the skeletal hierarchy.
• Figure 4: Left: Deformation of knee surrounded by the training grid. Upper image is the rest state (0,0), below image is (0,-90). Note that for knee there are only two degrees of freedom. Middle: Points on the grid selected for training data. The color of the node represents the distance to the boundary (red: close, green: distant). Right: Blue points have correct signed distance as the closest point lies on the origional boundary, the purple points have incorrect signed distance values.
• Figure 5: Training and validation losses for the Shallow SDF networks for subregions. $y-axis$ is log scaled.