November 9, 2014 Journal of Modern Optics Manuscript To appear in the Journal of Modern Optics Vol. 00, No. 00, 00 Month 20XX, 1–9 3D Reconstruction of Concave Surfaces using Polarisation Imaging A. Sohaib * , A.R. Farooq, J. Ahmed, L.N. Smith and M.L. Smith University of The West of England, Bristol, UK (Received 00 Month 20XX; final version received 00 Month 20XX) This paper presents a novel algorithm for improved shape recovery using polarisation based photometric stereo. The majority of previous research using photometric stereo involves 3D reconstruction using both the diffuse and specular components of light, however this paper suggests the use of the specular compo- nent only as it is the only form of light that comes directly off the surface without subsurface scattering or interreflections. Experiments were carried out on both real and synthetic surfaces. Real images were obtained using a polarisation based photometric stereo device while synthetic images generated using PovRay software. The results clearly demonstrate that the proposed method can extract three dimen- sional (3d) surface information effectively even for concave surfaces with complex texture and surface reflectance. Keywords: interreflections; photometric stereo; polarisation; 3D reconstruction 1. Introduction Photometric stereo is a technique that estimates the surface normals of an object by observing the change in reflected intensities of the the object under different lighting directions. In its basic form it assumes that the surface under consideration obeys the Lambertian reflectance model and the light incident on a surface is reflected from the same point. A surface is said to be Lambertian if the amount of light reflected by it is proportional to the cosine of the angle between the surface normal and light source direction. These assumptions lead to inaccuracies in estimating local surface normals when the surface under inspection exhibits complex reflectance and/ or is concave. A number of techniques have been used for combining polarisation information with photometric stereo to improve the recovery of 3D shape. Gary [1, 2], used Fresnel theory that relates the degree of polarisation of light with zenith angle and allows to calculate shape from diffuse polarisation. However this technique requires resolving a disambiguity in azimuth angle also the method requires capture of three images under 0,45, 90 degree orientation of polariser which increases the capture time and makes it less suitable for in vivo imaging of skin. Abhishek [3] used a multispectral light stage and polarised spherical gradient illumination to improve shape recovery of skin however their technique requires special arrangements of numerous light sources which makes it very expensive. Most of the techniques based on photometric stereo alone assume specular highlights as outliers [4–6] and are usually removed to get more accurate shape. This approach does improve the overall shape, as the Lambertian assumption in photometric stereo fits more closely to the object re- flectance after removal of specularities. However, this is only true for surfaces that are opaque and are not concave and they are also limited by the assumption that a specular pixel cannot exist in more than one image which is not true for a variety of materials with wide specular lobes. The * Corresponding author. Email: ali2.sohaib@live.uwe.ac.uk 1