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PHOTOMETRIC STEREO USING SPARSE
BAYESIAN
REGRESSION FOR GENERAL DIFFUSE
SURFACES
ABSTRACT
Most conventional algorithms for non-Lambertian photometric
stereo can be partitioned into two categories. The first category is built upon
stable outlier rejection techniques while assuming a dense Lambertian
structure for the inliers, and thus performance degrades when general
diffuse regions are present. The second utilizes complex reflectance
representations and non-linear optimization over pixels to handle non-
Lambertian surfaces, but does not explicitly account for shadows or other
forms of corrupting outliers. In this paper, we present a purely pixel-wise
photometric stereo method that stably and efficiently handles various non-
Lambertian effects by assuming that appearances can be decomposed into a
sparse, non-diffuse component (e.g., shadows, specularities, etc.) and a
diffuse component represented by a monotonic function of the surface

2. normal and lighting dot-product. This function is constructed using a
piecewise linear approximation to the inverse diffuse model, leading to
closed-form estimates of the surface normals and model parameters in the
absence of non-diffuse corruptions. The latter are modeled as latent
variables embedded within a hierarchical Bayesian model such that we may
accurately compute the unknown surface normals while simultaneously
separating diffuse from non-diffuse components. Extensive evaluations are
performed that show state-of-the-art performance using both synthetic and
real-world images.
EXISTING SYSTEM
The photometric stereo is a problem to recover surface normal of
a scene by inversely solving from a collection of observations under the
unknown set of parameters. The problem of course is that real images are
frequently contaminated with various non-diffuse effects as modeled
comparative theoretical properties of these approaches relevant to the
photometric stereo problem.
In this situation, the basic estimation problem reverts back that
automatically decomposes observed appearances into a continuous
piecewise linear diffuse component and a sparse, non-diffuse component for
capturing shadows, specularities, and other corruptions.
Proposed system
The proposed framework that pixel wise appearances are well-approximated
by a monotonic (and therefore invertible) function of the dot-product
between the surface normal and the lighting direction. We may then
consider the inverse representation of the image formation process, where

3. the unknown normal vector is now separated from the unknown monotonic
inverse reflectance function.
Advantage
The benefits from simple, efficient, pixel wise optimization, which is
easily amenable to parallel processing. Moreover it does not require the pre-processing
of specularities/shadows, careful initialization strategies, or
typical smoothness constraints for both object structure and reflectance,
which can disrupt the recovery of fine details.
MODULES
1. PIECEWISE LINEAR REGRESSION
2. PHOTOMETRIC STEREO VIA INVERSE PIECEWISE LINEAR SPARSE
REGRESSION
3. ROBUSTNESS TO SHADOWS AND IMAGE NOISE
4. MATHEMATICAL DIFFUSION
PIECEWISE LINEAR REGRESSION
In this module, the number of images, surface roughness (i.e.,
the ratio of specularities), shadow removal (i.e., whether or not a shadow
mask is used to remove zero-valued elements from the observed images),
and the presence of additional Gaussian noise. Note that when in use as
defined for each experiment, the shadow mask is applied equivalently to all
algorithms.

4. PHOTOMETRIC STEREO VIA INVERSE PIECEWISE LINEAR SPARSE
REGRESSION
In this module, we formulate the estimation of surface normals
using photometric stereo as a piecewise-linear sparse Bayesian regression
problem. Henceforth, we rely on the following assumptions.
1. Relative position between the camera and the object is fixed across
all images.
2. Object is illuminated by a point light source at infinity from varying
and known directions.
3. Camera view is orthographic, and the radiometric response function
is linear.
ROBUSTNESS TO SHADOWS AND IMAGE NOISE
In this module, we now evaluate the robustness of our method
against corruptions; shadows and image noise. We set two conditions for
evaluating the effects of
· Shadows (fixed specularities, no shadow removal, no image noise)
· Additive Gaussian image noise (fixed specularities, explicit shadow
removal, and varying amount of image noise).
· The ability to estimate surface normals without an explicit shadow mask
is important, since in practical situations shadow locations are not always
easy to be determined a priori.
MATHEMATICAL DIFFUSION

5. In this module, valid number of images for efficient recovery in
the presence of specularities. In this experiment, we vary the number of
images to estimate the minimum number required for effective recovery
when using the shadow mask with fixed surface roughness.
PHOTOMETRIC STEREO – ALGORITHM
Photometric stereo is a technique in computer vision for estimating
the surface normals of objects by observing that object under different
lighting conditions.
Photometric stereo has since been generalized to many other situations,
including non-uniform albedo, 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. Surface
normals define the local metric, using this observation defined a 3D face
recognition system based on the reconstructed metric without integrating
the surface. The metric of the facial surface is known to be robust to
expressions.
HARDWARE REQUIREMENTS
· System : Pentium IV 2.4 GHz.
· Hard Disk : 80 GB.
· Monitor : 15 VGA Colour.
· Mouse : Logitech.
· Ram : 512 MB.
SOFTWARE REQUIREMENTS

6. · Operating system : Windows 8 (32-Bit)
· Front End : Visual Studio 2010
· Coding Language : C#.NET

7. · Operating system : Windows 8 (32-Bit)
· Front End : Visual Studio 2010
· Coding Language : C#.NET