Introduction
Photometric stereo is a fascinating technique used to recover the 3D geometry of objects by analyzing images captured under different lighting conditions. By leveraging the relationships between light sources and image intensities, photometric stereo allows us to estimate surface normals and reconstruct the shape of objects. In this blog post, we will delve into the concept of photometric stereo, its underlying assumptions, challenges, and applications in computer graphics, robotics, and biomedical imaging.
Overview
Photometric stereo operates on the principle that the surface of an object is locally Lambertian, meaning the reflected light intensity is proportional to the cosine of the angle between the surface normal and the incident light direction. By capturing multiple images of an object under varying lighting conditions, we can analyze the image intensities to determine the surface normal at each point. With the surface normals known, we can reconstruct the 3D shape of the object.
Problem Statement
The objective of this project is to implement a standard photometric stereo algorithm. We will assume a Lambertian reflectance function and handle images with unknown and non-constant albedo. The algorithm will take multiple input images and the corresponding light source directions. Our task is to estimate the albedo map, surface normals, and reconstruct the height map from these inputs.
Dataset
The dataset consists of these images:
The first four images are synthetic, and the last four images are real.
Tasks
Preprocessing: Begin by scaling the image intensities into the [0, 1] range by dividing them by 255. Assume a constant strength of 1.0 for all light sources and camera parameter k as 1.0.
Shadow Handling: Apply the discussed method to eliminate equations corresponding to shadow points. Assume the intensity is zero for points in shadow.
Linear Equation Solving: Solve the linear equation Ax = b using the pseudo-inverse method. Compute the solution x = A+ b, where A+ is the pseudo-inverse matrix of A. The pseudo-inverse is defined as A+ = (AT A)–1 AT.
Surface Normals and Albedo Estimation: Read the images and estimate the surface normals and albedo map using the corresponding light source directions. Generate grayscale images for the estimated albedo map and three components of the surface normals (x, y, and z).
Height Map Reconstruction: Reconstruct the height map from the surface normals. Generate a grayscale image for the height map and a 3D surface plot using the actual height values.
Outputs
The implementation should produce the following outputs:
Grayscale image of the estimated albedo map: "{real/synthetic}_albedo.png"
Three grayscale images representing the three components of the estimated surface normals: "{real/synthetic}normal{x/y/z}.png"
Grayscale image of the estimated surface height map: "{real/synthetic}_height.png"
3D surface plot of the estimated surface height map: "{real/synthetic}_height_3D.jpg"
Photometric stereo offers a powerful approach to recover the 3D geometry of objects based on images captured under different lighting conditions. By estimating surface normals and reconstructing height maps, we can gain insights into the shape and structure of objects. This project has explored the implementation of a photometric stereo algorithm, highlighting the estimation of albedo maps, surface normals, and height maps. The outputs provide visual representations of these estimations, enabling a deeper understanding of the object's geometry. Photometric stereo holds significant potential in computer graphics, robotics, and biomedical imaging, paving the way for realistic 3D models, object recognition, and biomedical tissue reconstruction.
If you need implementation for the above problem or any of its variants, feel free to contact us.
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