Single View Homography Estimation for an Inclined Textured Planar Surface: Overcoming the Inverse and Ill-Posed Challenge!

Pooja Kumari, Sukhendu Das

Abstract: Homography estimation is a crucial step in many computer vision problems involving the planar transformation of an image from one view to another. Generally, from two image views of a scene with a planar patch, one can compute the homography matrix (H) using Direct Linear Transformation (DLT) or its variants. In this study, we work on the inverse scenario to solve an ill-posed problem, where given only a single image (<Formula format="inline"><TexMath><?TeX $I_{\tau }^{P}$?></TexMath><AltText>Math 1</AltText><File name="icvgip23-2-inline1" type="svg"/></Formula>) of an inclined textured planar surface, we attempt to estimate both H and the orthogonal view (<Formula format="inline"><TexMath><?TeX $I_{\tau }^{O}$?></TexMath><AltText>Math 2</AltText><File name="icvgip23-2-inline2" type="svg"/></Formula>) of the planar surface. We propose to solve this problem of homography Estimation using an optimization framework. To the best of our knowledge, there has barely been any work done on this inverse scenario of homography estimation from only a single image view. The research presented in this paper successfully achieves image rectification and homography computation by assuming a perspective transformation on an upright planar patch when viewed by a camera placed exactly in front of it. A cost function with suitable constraints is utilized to refine homography estimation. Experimental results reveal the efficiency of the proposed approach in the case of images of checkerboard and other textured planar surfaces (real-world images with lines and other prominent textures).