Photometric stereo for micro-scale shape reconstruction

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Virginia Tech

This dissertation proposes an approach for 3D micro-scale shape reconstruction using photometric stereo (PS) with surface normal integration (SNI). Based on the proposed approach, a portable cost-effective stationary system is developed to capture 3D shapes in the order of micrometer scale. The PS with SNI technique is adopted to reconstruct 3D microtopology since this technique is highlighted for its capability to reproduce fine surface details at pixel resolution. Furthermore, since the primary hardware components are merely a camera and several typical LEDs, the system based on PS with SNI can be made portable at low cost.

The principal contributions are three folds. First, a PS method based on dichromatic reflectance model (DRM) using color input images is proposed to generalize PS applicable to a wider range of surfaces with non-Lambertian reflectances. The proposed method not only estimates surface orientations from diffuse reflection but also exploits information from specularities owing to the proposed diffuse-specular separation algorithm. Using the proposed PS method, material-dependent features can be simultaneously extracted in addition to surface orientations, which offers much richer information in understanding the 3D scene and poses more potential functionalities, such as specular removal, intrinsic image decomposition, digital relighting, material-based segmentation, material transfer and material classification.

The second contribution is the development of an SNI method dealing with perspective distortion. The proposed SNI is performed on the image plane instead of on the target surface as did by orthographic SNI owing to the newly derived representation of surface normals. The motivation behind the representation is from the observation that spatially uniform image points are simpler for integration than the non-uniform distribution of surface points under perspective projection. The new representation is then manipulated to the so-called log gradient space in analogy to the gradient space in orthographic SNI. With this analogy, the proposed method can inherit most past algorithms developed for orthographic SNI. By applying the proposed SNI, perspective distortion can be efficiently tackled with for smooth surfaces. In addition, the method is PS-independent, which can keep the image irradiance equation in a simple form during PS.

The third contribution is the design and calibration of a 3D micro-scale shape reconstruction system using the derived PS and SNI methods. This system is originally designed for on-site measurement of pavement microtexture, while its applicability can be generalized to a wider range of surfaces. Optimal illumination was investigated in theory and through numerical simulations. Five different calibrations regarding various aspects of the system were either newly proposed or modified from existing methods. The performances of these calibrations were individually evaluated. Efficacy of the developed system was finally demonstrated through comprehensive comparative studies with existing systems. Its capability for on-site measurement was also confirmed.

3D Reconstruction, Photometric Stereo, Surface Normal Integration, Image Formation