Analytic Reconstruction of Transparent and Opaque Surfaces from Texture Images Mohamad Ivan Fanany and Itsuo Kumazawa Imaging Science and Engineering, Tokyo Institute of Technology fanany@isl.titech.ac.jp Abstract. This paper addresses the problem of reconstructing non- overlapping transparent and opaque surfaces from multiple view images. The reconstruction is attained through progressive refinement of an initial 3D shape by minimizing the error between the images of the object and the initial 3D shape. The challenge is to simultaneously reconstruct both the transparent and opaque surfaces given only a limited number of images. Any refinement methods can theoretically be applied if analytic relation between pixel value in the training images and vertices position of the ini- tial 3D shape is known. This paper investigates such analytic relations for reconstructing opaque and transparent surfaces. The analytic relation for opaque surface follows diffuse reflection model, whereas for transpar- ent surface follows ray tracing model. However, both relations can be con- verged for reconstruction both surfaces into texture mapping model. To improve the reconstruction results several strategies including regulariza- tion, hierarchical learning, and simulated annealing are investigated. 1 Introduction Many methods acquire high quality 3D shape of opaque object with a diffuse surface [3], but still not many methods acquire 3D shape of transparent ob- ject. Usually the reconstruction of transparent object is dealt exclusively from the reconstruction of opaque object, and vice versa. This is because the percep- tion of transparent surface is a hard vision problem. Transparent surface lacks of body and surface reflections, is suffered much from inter-reflection [4], and lacks of naturally-occurring shape. The only potential sources of surface informa- tion are specular highlights, environmental reflections, and refractive distortion, whereas depth information is almost completely unavailable [5]. Only recently, some prospective techniques for modeling transparent surface have emerged. We categorize these methods into two groups as follows. The first group elaborates as much the surface related features as possible to explicitly define the surface’s shape. It includes a method to recover the shape of water surface [6], and a transparent surface, projected by a light stripe, using genetic algorithm [7]. The second group elaborates as much ways as possible to synthesize a realistic image of transparent object without using any 3D shape information. It includes a method called environment matting for capturing the optical behavior of transparent surface from known and controlled background J. Mart´ ı et al. (Eds.): IbPRIA 2007, Part II, LNCS 4478, pp. 380–387, 2007. c  Springer-Verlag Berlin Heidelberg 2007