Stroke-Based Surface Reconstruction

Abstract

In this paper, we present a surface reconstruction via 2D strokes and a vector field on the strokes based on a two-step method. In the first step, from sparse strokes drawn by artists and a given vector field on the strokes, we propose a nonlinear vector interpolation combining total variation (TV) and H^ regularization with a curl-free constraint for obtaining a dense vector field. In the second step, a height map is obtained by integrating the dense vector field in the first step. Jump discontinuities in surface and discontinuities of surface gradients can be well reconstructed without any surface distortion. We also provide a fast and efficient algorithm for solving the proposed functionals. Since vectors on the strokes are interpreted as a projection of surface gradients onto the plane, different types of strokes are easily devised to generate geometrically crucial structures such as ridge, valley, jump, bump, and dip on the surface. The stroke types help users to create a surface which they intuitively imagine from 2D strokes. We compare our results with conventional methods via many examples. . sg (H. S. Seah) http://www.global-sci.org/nmtma 297 ©2013 Global-Science Press 298 J. Hahn et al. or shape-from-shading [9,10], or geometric constraints defined by 3D curve network [11], the task of 3D model reconstruction from 2D line drawings is more challenging than imagebased 3D reconstruction. A lot of research results have been achieved towards this challenging task based on contours [2], hidden contours [3], symmetric sketch pairs [12], and structured annotations [13]. The models created by these systems are limited in structures of shape. Moreover, surface details such as the crease structure are not considered in these systems. Note that the crease structure can be added by surficial augmentation techniques [14]. Motivated by the above mentioned works, we are targeting at a sketchbased modeling system which can model complex 3D objects with simple sketches. As the first attempt to this direction, we present our research achievement on surface height reconstruction via 2D strokes and a vector field on the strokes. Many surface reconstruction algorithms from surface gradients [15-18] enforce the integrability for producing correct surface heights. For single-view modeling, the authors [19] used a constrained optimization with many types of geometrical constraints. The authors [20] showed that the method in [19] requires a lot of user interactions to provide enough constraints for modeling a desirable surface. Another single-view modeling system [21] used a close form method to reconstruct curved 3D surfaces based on apparent contour, infiation constraints, and normal specification in the parameter space. Recently, the authors [22] highlighted that the algorithms in [19][20][21] have difficulties in solving three problems in surface-from-gradients: handling sparse gradients, preserving sharp features, and preventing surface distortion. To solve these problems, Gaussian kernel approach without discrete integrabi...

A hybrid approach for character modeling using geometric primitives and shape-from-shading algorithm

“…In this paper the author discusses in detail the philosophy behind generating 3D surfaces from shaded/lighted images. Several SFS techniques have taken inspiration from Koenderink work such as [4], [5], and [6].…”

Sparse-Data Based 3D Surface Reconstruction for Cartoon and Map

“…Reconstructing an image from its little information available is a challenging but interesting task for image processing, which has attracted much attention over the years, finding applications in many areas where, for instance, information are available only in the form of a small number of level lines or isolated points. Two of its well known applications are the sketch based design where three dimensional figures or structures are designed from sketches made by an artist or a computer program, and the surface reconstruction where three dimensional surface is reconstructed from its level lines, see for instance two recent publications [11,15], for a review on the subject. In this paper, we are interested surfaces that are moderately complex, in the sense that they contain both structured and unstructured geometries, man made or natural, and feature both kinks (sharp twists) and creases (folds).…”

“…A different class of models, based on the total variation minimization, turned out to be much more effective, cf. [11]. The model presented in these two papers is based on interpolating normal vectors under the curl-free constraint and then reconstructing the 3D surface from the obtained vector field.…”

“…[6,31,12,16] for further works on TV-Stokes models. The model of [11] performs very well in preserving both edges and crease structures, however, it requires prior information on the vectors, e.g. the length of vectors [34,11], which are not always available.…”

“…e.g. [11,15]. However, the use of such information, in these papers, has been done somewhat indirectly, that is by first constructing a smooth vector field from the vector information available on the level lines, that is in a prepossessing step, and then using the new vector field in the reconstruction step.…”