Representing 3D shape and location

The 3D shape of an object and its 3D location have traditionally thought of as very separate entities, although both can be described within a single 3D coordinate frame. Here, 3D shape and location are considered as two aspects of a view-based approach to representing depth, avoiding the use of 3D coordinate frames

Similarity solutions for slender dry patches with thermocapillarity

We use the lubrication approximation to investigate slender dry patches in an infinitely wide film of viscous fluid flowing steadily on an inclined plane that is either heated or cooled relative to the surrounding atmosphere. Four non-isothermal situations in which thermocapillary effects play a significant role are considered. Similarity solutions describing a thermocapillary-driven flow with a dry patch that is widening or narrowing due to either gravitational or surface-tension effects on a non-uniformly heated or cooled substrate are obtained, and we present examples of these solutions when the substrate temperature gradient depends on the longitudinal coordinate according to a general power law. When gravitational effects are strong the solution contains a free parameter, and for each value of this parameter there is a unique solution representing both a narrowing pendent dry patch and a widening sessile dry patch, whose transverse profile has a monotonically increasing shape. When surface tension effects are strong the solution also contains a free parameter, and for each value of this parameter there is both a unique solution representing a narrowing dry patch, whose transverse profile has a monotonically increasing shape, and a one-parameter family of solutions representing a widening dry patch, whose transverse profile has a capillary ridge near the contact line and decays in an oscillatory manner far from it. Similarity solutions are also obtained for both a gravity-driven and a constant surface- shear-stress-driven flow with a dry patch that is widening or narrowing due to thermocapillarity on a uniformly heated or cooled substrate. The solutions in both cases contain a free parameter, and for each value of this parameter there is a unique solution representing both a narrowing dry patch on a heated substrate and a widening dry patch on a cooled substrate, whose transverse profile has a monotonically increasing shape

SurfNet: Generating 3D shape surfaces using deep residual networks

3D shape models are naturally parameterized using vertices and faces, \ie, composed of polygons forming a surface. However, current 3D learning paradigms for predictive and generative tasks using convolutional neural networks focus on a voxelized representation of the object. Lifting convolution operators from the traditional 2D to 3D results in high computational overhead with little additional benefit as most of the geometry information is contained on the surface boundary. Here we study the problem of directly generating the 3D shape surface of rigid and non-rigid shapes using deep convolutional neural networks. We develop a procedure to create consistent `geometry images' representing the shape surface of a category of 3D objects. We then use this consistent representation for category-specific shape surface generation from a parametric representation or an image by developing novel extensions of deep residual networks for the task of geometry image generation. Our experiments indicate that our network learns a meaningful representation of shape surfaces allowing it to interpolate between shape orientations and poses, invent new shape surfaces and reconstruct 3D shape surfaces from previously unseen images.Comment: CVPR 2017 pape

Spheres and Prolate and Oblate Ellipsoids from an Analytical Solution of Spontaneous Curvature Fluid Membrane Model

An analytic solution for Helfrich spontaneous curvature membrane model (H. Naito, M.Okuda and Ou-Yang Zhong-Can, Phys. Rev. E {\bf 48}, 2304 (1993); {\bf 54}, 2816 (1996)), which has a conspicuous feature of representing the circular biconcave shape, is studied. Results show that the solution in fact describes a family of shapes, which can be classified as: i) the flat plane (trivial case), ii) the sphere, iii) the prolate ellipsoid, iv) the capped cylinder, v) the oblate ellipsoid, vi) the circular biconcave shape, vii) the self-intersecting inverted circular biconcave shape, and viii) the self-intersecting nodoidlike cylinder. Among the closed shapes (ii)-(vii), a circular biconcave shape is the one with the minimum of local curvature energy.Comment: 11 pages, 11 figures. Phys. Rev. E (to appear in Sept. 1999