Controllable Shape Modeling with Neural Generalized Cylinder

TL;DR

This work proposes neural generalized cylinder (NGC) for explicit manipulation of NSDF, which is an extension of traditional generalized cylinder (GC) which defines a central curve first and assign neural features along the curve to represent the profiles.

Abstract

Neural shape representation, such as neural signed distance field (NSDF), becomes more and more popular in shape modeling as its ability to deal with complex topology and arbitrary resolution. Due to the implicit manner to use features for shape representation, manipulating the shapes faces inherent challenge of inconvenience, since the feature cannot be intuitively edited. In this work, we propose neural generalized cylinder (NGC) for explicit manipulation of NSDF, which is an extension of traditional generalized cylinder (GC). Specifically, we define a central curve first and assign neural features along the curve to represent the profiles. Then NSDF is defined on the relative coordinates of a specialized GC with oval-shaped profiles. By using the relative coordinates, NSDF can be explicitly controlled via manipulation of the GC. To this end, we apply NGC to many non-rigid deformation tasks like complex curved deformation, local scaling and twisting for shapes. The comparison on shape deformation with other methods proves the effectiveness and efficiency of NGC. Furthermore, NGC could utilize the neural feature for shape blending by a simple neural feature interpolation.

Figures (13)

• Figure 1: Overview of NGC for shape fitting, deformation, and blending. To convert a input mesh to NGC representation, we first prepare the skeleton curves and generate corresponding generalized cylinders (GCs). Then we sample points and their signed distances within the GCs to train a neural SDF network, where the neural SDF is defined in the relative coordinate systems of the GCs. Finally, the reconstructed mesh can be extracted by Marching Cubes. For deformation, because the neural SDF is defined with relative coordinates on the GCs, we can directly manipulate the GCs in order to deform the shape. For blending, after training our NGC network on a collection of shapes, we can blend the part from one shape into another shape by simply replacing and interpolating their learned neural features.
• Figure 2: Illustration of the relative coordinate system used in our method. Red, green, and blue indicate the x, y, and z axes, respectively. The position of a point can be specified by its relative coordinates, which are invariant to the "shape" of the GC.
• Figure 3: (a) An implicit field (visualized with its 0-isosurface) is defined on the relative coordinates of a GC. (b) Canonical cylinder. (c) The implicit field will change according to changes of the GC.
• Figure 4: Visualization of profiles for classic GC and NGC. Classic GC stores a limited number of profiles for each shape. The profiles between two existing profiles are obtained via profile interpolation, which is challenging when the two profiles are with different topology. The topological difference between profiles could be caused by non-convex shape as in (a) or high genus as in (b). In contrast, NGC represents all profiles as continuous neural SDF, thereby avoiding the interpolation challenge.
• Figure 5: The flexibility of skeleton definition in NGC. Bottom: we can extract the skeleton curves and generate a compact GC covering, and represent the shape with NGC. Top: alternatively, we can use just one large GC (with one curve) to represent the shape. The two reconstructed meshes are similar in visual quality, but the difference is in controllability. More complex control of the shape is supported by the finer GCs.