International Journal of Multimedia and Ubiquitous Engineering Vol.10, No.9 (2015), pp.199-210 http://dx.doi.org/10.14257/ijmue.2015.10.9.21 ISSN: 1975-0080 IJMUE Copyright ⓒ 2015 SERSC Shape Modification from Endoscope Images by Regression Analysis Yuji Iwahori 1* , Seiya Tsuda 1* , Aili Wang 2 , Robert J. Woodham 3 , M. K. Bhuyan 4 , and Kunio Kasugai 5 1 Dept. of Computer Science, Chubu University, 487-8501 Japan 2 Dept. of Measurement & Control Technology and Instrumentations of Heilongjiang, Harbin University of Science and Technology, China 3 Dept. of Computer Science, University of British Columbia, Canada V6T 1Z4 4 Dept. of Electronics and Electrical Engineering, IIT Guwahati, 781039 India 5 Dept. of Gastroenterology, Aichi Medical University, 480-1195 Japan *Corresponding author: Yuji Iwahori (iwahori@cs.chubu.ac.jp) Abstract The VBW (Vogel-Breuß-Weickert) model is proposed as a method to recover 3-D shape under point light source illumination and perspective projection. However, the VBW model recovers relative, not absolute, shape. Here, shape modification is introduced to recover the exact shape. Modification is applied to the output of the VBW model. First, a local brightest point is used to estimate the reflectance parameter from two images obtained with movement of the endoscope camera in depth. A Lambertian sphere image is generated using the estimated reflectance parameter and VBW model is applied for a sphere. Regression analysis is introduced to improve the surface gradients, where linear coefficients can be obtained using true values of gradient parameters with a generated sphere. Depth can then be recovered using the modified gradient parameters. Performance of the proposed approach is confirmed via computer simulation and real experiment. Keywords: Endoscope Image, VBW Model, Regression Analysis, Shape Modification, Reflection Factor 1. Introduction Endoscopy allows medical practitioners to observe the interior of hollow organs and other body cavities in a minimally invasive way. Sometimes, diagnosis requires assessment of the 3-D shape of the observed tissue. For example, the pathological condition of a polyp often is related to its geometrical shape. Medicine is an important area of application of computer vision technology. Many approaches are based on stereo vision [1]. However, the size of the endoscope becomes large and this imposes a burden on the patient. Here, we consider a general purpose endoscope, of the sort still most widely used in medical practice. Shape recovery from endoscope images is considered. Shape from shading (SFS) [2] and Fast Marching Method (FMM) [3] based SFS approach [4] are proposed. These approaches assume orthographic projection. An extension of FMM to perspective projection is proposed in [5]. Further extension of FMM to both point light source illumination and perspective projection is proposed in [6]. Recent extensions include generating a Lambertian image from the original multiple color images [7-8]. Application of FMM includes solution [9] under oblique illumination using neural network learning [10]. Most of the previous approaches treat the reflectance parameter as a known constant. The problem is that it is impossible to estimate the reflectance parameter from