CraGL: Computational Reality, Creativity and Graphics Lab

Interacting with Self-Similarity

Josef Graus, Alec Jacobson, Yotam Gingold
Computer-Aided Design (CAD) volume 130, 2021.

Paper: PDF, 600dpi images (2 MB) | PDF, full size images (12 MB)

Code: GitHub

An illustration of geometry propagation using our curve propagation: (Left to right) (1) A single ring is drawn on a finger of the hand; (2) Additional ringplacements are suggested; (3) The ring placements are exported to Blender; (4) Complex geometry (ring pops) are placed and aligned according to the exportedcurves (manually, as an illustrative application). An illustration of geometry propagation using our curve propagation: (Left to right) (1) A single ring is drawn on a finger of the hand; (2) Additional ringplacements are suggested; (3) The ring placements are exported to Blender; (4) Complex geometry (ring pops) are placed and aligned according to the exportedcurves (manually, as an illustrative application).

Abstract:

Shape similarity is a fundamental problem in geometry processing, enabling applications such as surface correspondence, segmentation, and edit propagation. For example, a user may paint a stroke on one finger of a model and desire the edit to propagate to all fingers. Automatic approaches have difficulty matching user expectations, either due to an algorithm's inability to guess the scale at which the user is intending to edit or due to underlying deficiencies in the similarity metric (e.g., semantic information not present in the geometry).

We propose an approach to interactively design self-similarity maps. We investigate two primitive operations, useful in a variety of scenarios: region and curve similarity. Users select example similar and dissimilar regions. Starting with an automatically generated multi-scale shape signature, our approach solves for a scale parameter and thresholds that group the example regions as specified. We propose a new Smooth Shape Diameter Signature (SSDS) as a more efficient alternative to the Heat or Wave Kernel Signature. If no such parameters can be found, our approach modifies the shape signature itself. Given a curve drawn on the surface, we perform hybrid discrete/continuous optimization to find similar curves elsewhere.

We apply our approach for interactive editing scenarios: propagating mesh geometry, patterns duplication, and segmentation.

Demonstration Video MP4 (16 MB):

BibTeX (or see the publisher's page): 

@article{Graus:2021:ISS,
  title    = {Interacting with Self-Similarity},
  journal  = {Computer-Aided Design},
  volume   = {130},
  pages    = {102931},
  year     = {2021},
  issn     = {0010-4485},
  doi      = {https://doi.org/10.1016/j.cad.2020.102931},
  url      = {http://www.sciencedirect.com/science/article/pii/S001044852030124X},
  author   = {Josef Graus and Alec Jacobson and Yotam Gingold},
  keywords = {Shape analysis, Signature, Interaction, Similarity}
}

Funding: This work was supported in part by the United States National Science Foundation (IIS-1453018), a Google research award, and a gift from Adobe Systems Inc.