Photometric stereo

Photometric stereo is a technique in computer vision for estimating the surface normals of objects by observing that object under different lighting conditions. It is based on the fact that the amount of light reflected by a surface is dependent on the orientation of the surface in relation to the light source and the observer. By measuring the amount of light reflected into a camera, the space of possible surface orientations is limited. Given enough light sources from different angles, the surface orientation may be constrained to a single orientation or even overconstrained. The technique was originally introduced by Woodham in 1980. The special case where the data is a single image is known as shape from shading, and was analyzed by B. K. P. Horn in 1989. Photometric stereo has since been generalized to many other situations, including extended light sources and non-Lambertian surface finishes. Current research aims to make the method work in the presence of projected shadows, highlights, and non-uniform lighting. Under Woodham's original assumptions — Lambertian reflectance, known point-like distant light sources, and uniform albedo — the problem can be solved by inverting the linear equation , where is a (known) vector of observed intensities, is the (unknown) surface normal, and is a (known) matrix of normalized light directions. This model can easily be extended to surfaces with non-uniform albedo, while keeping the problem linear. Taking an albedo reflectivity of , the formula for the reflected light intensity becomes: If is square (there are exactly 3 lights) and non-singular, it can be inverted, giving: Since the normal vector is known to have length 1, must be the length of the vector , and is the normalised direction of that vector. If is not square (there are more than 3 lights), a generalisation of the inverse can be obtained using the Moore–Penrose pseudoinverse, by simply multiplying both sides with giving: After which the normal vector and albedo can be solved as described above.

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Related publications (1)

Leveraging Spatial and Photometric Context for Calibrated Non-Lambertian Photometric Stereo

Pascal Fua, Engin Türetken, David Honzátko

The problem of estimating a surface shape from its observed reflectance properties still remains a challenging task in computer vision. The presence of global illumination effects such as inter-reflections or cast shadows makes the task particularly difficult for non-convex real-world surfaces. State-of-the-art methods for calibrated photometric stereo address these issues using convolutional neural networks (CNNs) that primarily aim to capture either the spatial context among adjacent pixels or the photometric one formed by illuminating a sample from adjacent directions. In this paper, we bridge these two objectives and introduce an efficient fully-convolutional architecture that can leverage both spatial and photometric context simultaneously. In contrast to existing approaches that rely on standard 2D CNNs and regress directly to surface normals, we argue that using separable 4D convolutions and regressing to 2D Gaussian heat-maps severely reduces the size of the network and leads to more stable predictions. Our experimental results on a real-world photometric stereo benchmark show that the proposed approach outperforms the existing published methods in accuracy. The source code for our method is available at https://github.com/DawyD/UNet-PS-4D.

IEEE COMPUTER SOC2021