A non-Lambertian photometric stereo under perspective projection
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Frontiers of Information Technology & Electronic Engineering www.jzus.zju.edu.cn; engineering.cae.cn; www.springerlink.com ISSN 2095-9184 (print); ISSN 2095-9230 (online) E-mail: [email protected]
A non-Lambertian photometric stereo under perspective projection∗ Min LI†1 , Chang-yu DIAO†‡2 , Duan-qing XU1 , Wei XING1 , Dong-ming LU1 1College
of Computer Science and Technology, Zhejiang University, Hangzhou 310027, China
2School
of Art and Archeology, Zhejiang University, Hangzhou 310027, China † E-mail:
[email protected]; [email protected]
Received Mar. 19, 2019; Revision accepted Aug. 21, 2019; Crosschecked Nov. 12, 2019
Abstract: Under the perspective projection assumption, non-Lambertian photometric stereo is a highly non-linear problem. In this study, we present an optimized framework for reconstructing the surface normal and depth with non-Lambertian reflection models under perspective projection. By decomposing the images into diffuse and specular components, we compute the surface normal and reflectance simultaneously. We also propose a variational formulation that is robust and useful for surface reconstruction. The experiments show that our method accurately reconstructs both the surface shape and reflectance of colorful objects with non-Lambertian surfaces. Key words: Photometric stereo; Three-dimensional reconstruction; Perspective projection; Image decomposition https://doi.org/10.1631/FITEE.1900156 CLC number: TP391.4
1 Introduction Photometric stereo is a technique for recovering the surface normal and reflectance using the reflectance model under different lighting conditions. Since Woodham (1979) first introduced photometric stereo for Lambertian scenes under orthogonal projection, the extension to real-world conditions, such as non-Lambertian appearances under perspective projection, has drawn significant interest. The reconstruction of the surface normal and depth can be used to provide highly detailed threedimensional (3D) models in many applications, such as reverse engineering and digital preservation of cultural heritage. ‡ *
Corresponding author
Project supported by the Technological Program of Cultural Relics Preservation of Zhejiang Province, China, the Key Research and Development Program of Zhejiang Province, China (No. 2018C03051), and the National Standard Development Program of Cultural Relics Protection of China (No. 581250T0170B) ORCID: Min LI, http://orcid.org/0000-0003-4732-6457; Chang-yu DIAO, http://orcid.org/0000-0001-7744-0889 c Zhejiang University and Springer-Verlag GmbH Germany, part of Springer Nature 2019
The error of surface reflectance and depth reconstruction brought by the complex surface reflectance property is one of the most significant difficulties that prevent photometric stereo from being practical. Most previous photometric stereo algorithms focus only on computing surface normals with non-Lambertian scenes under orthogonal projection. One class of such methods assumes a perfect Lambertian model by adopting outlier rejection approaches to handle all non-Lambertian
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