1.1 Background
Recently, the requirement of digitizing 3D models and estimating surface parameters from real objects is increased dramatically. They are extensively used in computer graphics, computer vision, and other analysis applications. 3D acquisition can be categorized into several principal approaches: passive stereo, active stereo, shape from shading, photometric stereo, etc. Each of them has its advantages and disadvantages.
Passive stereo methods use multiple images captured from difference viewpoints. Then, they estimate the correspondences between images and calculate 3D positions by intersecting corresponding pairs. The major benefit of passive stereo is easy to implement and it requires only two or more cameras. But, estimating the exact correspondence between images is difficult, and therefore the accuracy of the data may be unreliable.
Active stereo utilizes additional light sources or laser projectors for scanning, and thus the correspondences between two images are easier to be acquired. The accuracy of active stereo approaches is therefore relatively high. On the other hand, the active stereo systems usually require additional projection devices which are usually heavy and costly. However, the surface details of non-lamertian material objects are usually difficult to be acquired by active stereo or passive stereo since correspondences on details are usually ambiguous and the reflection properties are not taken into account.
Shape from shading and photometric stereo methods make use of shading information to recover the 3D shape. Most works on photometric stereo are based on the lambertian model.
They usually use a single view direction, but various lighting directions. The normal estimation then become a simple linear least-square problem. But the accuracy may be not reliable because the objects are not always with lambertian reflection properties and reconstructing surface from normal variations is ill-condition. Shape from shading (SFS) uses intensity variation of a single image and known lighting conditions to recovery 3D shape. The problem of finding correspondences can be avoided in shape from shading, but the solution of shape from shading relies on image quality and accurate reflectance models. Shapes recovered by shape from shading are usually tainted due to input noise or simplified reflectance models.
1.2 Motivation
For accurate reconstruction of 3D models, combining both positions and reflectance properties (shading information) is a practical method. Diego (2005) et al. [1] proposed an impressive approach to combine 3D positions and normals for precise 3D geometry. They measured the positions and normals by a structured light system and a photometric stereo method respectively. In order to efficiently combine the positions and normals by linear cross products, they assume the objects are with lambertian properties and only use lambertian reflectance model to acquire normals.
However, non-lambertian and sub-surface scattering materials are commonly found in the natured world. The lambertian reflectance model is insufficient to represent the greater part of objects. A simpler non-lambertian model for shape recovery is purposed by Tianli (2004) et al [2]. They apply the Phong reflectance model to model the surface reflectance and then used visual hull to find the initial shape. Then, an optimization approach, conjugate gradient, is
purposed to find the shape and reflectance parameters that fit multiple views images.
Although, the specular reflection is taken into account and visual hull is used for initial positions. The sub-surface scattering material objects are still not easy to be reconstructed by their method. This problem is still a bottleneck of the reconstruction. In general, to scan these objects, operators usually apply powders or paints on the surface to avoid dealing with non-lambertian properties. The painting process is inconvenient and not applicable for valuable objects.
1.3 Purpose
To tackle the above mentioned problems, in this thesis, we present the use of the stereo structured light to acquire the initial positions. And then, Phong model and Bidirectional Scattering Surface Reflectance Distribution Function model (BSSRDF) are used to optimize the positions of scanned 3D geometry and also acquire the reflectance properties. For the BSSRDF model, Jensen et al. (2001) [3] introduced a dipole diffusion approximation for light scattering. This approximation uses an extension to diffusion theory.
We make use of these models to compensate scanned 3D geometry of the non-lambertian or sub-surface scattering objects. Our method is performed in three steps: First, a projective stereo structured light system is used to acquire the initial positions and normals. Second, assume the light and camera locations are known, we simplify the Phong model and Jensen’s model. Then, we use the simplify models to acquire the optimize reflectance parameters. The optimization method we apply is conjugate gradient. It minimizes the difference between synthesized images and the real images. Last, using the estimated reflectance parameters, we can further optimize the position with conjugate gradient. In order to get a more precise shape
most accurate 3D model and reflectance properties.
1.4 Contribution
In the thesis, we propose an approach to combine 3D scanned data and reflectance properties for precise 3D surface. The primary research goals and features are addressed as follows:
(a) Improving the scanning accuracy of non-lambertian and sub-surface scattering objects.
(b) Utilizing only inexpensive devices.
(c) The method is not only reconstructing the shape but also estimating the reflectance properties. We can use them to render the object from different views and lighting conditions.
1.5 System Overview
Our goal is to recover a high quality 3D geometry from images. We combined the positions measured by structured light system and Phong or BSSRDF reflectance model to optimize the reconstructed result. We separate our method into three steps, and the system overview is as follows:
1.6 Organization
This thesis is organized as follows. Chapter 2 is about related work, we will review the literature on structured light systems, BSSRDF reflectance model, and combining techniques.
Chapter 3, 4 propose our method of surface detail optimization. Various issues such as initialization, reflectance model, and stereo structured light system will also be discussed.
Chapter 5 shows the experiment results on real and synthetic objects. Chapter 6 presents the conclusion and future work.
Fig.1 System overview.
reflection parameters
3D geometry Structured light
reconstruction
Input Images, Camera & Lighting
Info.
Optimization