656 research outputs found
Analysis of surface parametrizations for modern photometric stereo modeling
Tridimensional shape recovery based on Photometric Stereo (PS) recently received a strong improvement due to new mathematical models based on partial differential irradiance equation ratios. This modern approach to PS faces more realistic physical effects among which light attenuation and radial light propagation from a point light source. Since the approximation of the surface is performed with single step method, accurate reconstruction is prevented by sensitiveness to noise. In this paper we analyse a well-known parametrization of the tridimensional surface extending it on any auxiliary convex projection functions. Experiments on synthetic data show preliminary results where more accurate reconstruction can be achieved using more suitable parametrization specially in case of noisy input images
Variational Uncalibrated Photometric Stereo under General Lighting
Photometric stereo (PS) techniques nowadays remain constrained to an ideal
laboratory setup where modeling and calibration of lighting is amenable. To
eliminate such restrictions, we propose an efficient principled variational
approach to uncalibrated PS under general illumination. To this end, the
Lambertian reflectance model is approximated through a spherical harmonic
expansion, which preserves the spatial invariance of the lighting. The joint
recovery of shape, reflectance and illumination is then formulated as a single
variational problem. There the shape estimation is carried out directly in
terms of the underlying perspective depth map, thus implicitly ensuring
integrability and bypassing the need for a subsequent normal integration. To
tackle the resulting nonconvex problem numerically, we undertake a two-phase
procedure to initialize a balloon-like perspective depth map, followed by a
"lagged" block coordinate descent scheme. The experiments validate efficiency
and robustness of this approach. Across a variety of evaluations, we are able
to reduce the mean angular error consistently by a factor of 2-3 compared to
the state-of-the-art.Comment: Haefner and Ye contributed equall
Analysis and approximation of some Shape-from-Shading models for non-Lambertian surfaces
The reconstruction of a 3D object or a scene is a classical inverse problem
in Computer Vision. In the case of a single image this is called the
Shape-from-Shading (SfS) problem and it is known to be ill-posed even in a
simplified version like the vertical light source case. A huge number of works
deals with the orthographic SfS problem based on the Lambertian reflectance
model, the most common and simplest model which leads to an eikonal type
equation when the light source is on the vertical axis. In this paper we want
to study non-Lambertian models since they are more realistic and suitable
whenever one has to deal with different kind of surfaces, rough or specular. We
will present a unified mathematical formulation of some popular orthographic
non-Lambertian models, considering vertical and oblique light directions as
well as different viewer positions. These models lead to more complex
stationary nonlinear partial differential equations of Hamilton-Jacobi type
which can be regarded as the generalization of the classical eikonal equation
corresponding to the Lambertian case. However, all the equations corresponding
to the models considered here (Oren-Nayar and Phong) have a similar structure
so we can look for weak solutions to this class in the viscosity solution
framework. Via this unified approach, we are able to develop a semi-Lagrangian
approximation scheme for the Oren-Nayar and the Phong model and to prove a
general convergence result. Numerical simulations on synthetic and real images
will illustrate the effectiveness of this approach and the main features of the
scheme, also comparing the results with previous results in the literature.Comment: Accepted version to Journal of Mathematical Imaging and Vision, 57
page
Geometric and photometric affine invariant image registration
This thesis aims to present a solution to the correspondence problem for the registration
of wide-baseline images taken from uncalibrated cameras. We propose an affine
invariant descriptor that combines the geometry and photometry of the scene to find
correspondences between both views. The geometric affine invariant component of the
descriptor is based on the affine arc-length metric, whereas the photometry is analysed
by invariant colour moments. A graph structure represents the spatial distribution of the
primitive features; i.e. nodes correspond to detected high-curvature points, whereas arcs
represent connectivities by extracted contours. After matching, we refine the search for
correspondences by using a maximum likelihood robust algorithm. We have evaluated
the system over synthetic and real data. The method is endemic to propagation of errors
introduced by approximations in the system.BAE SystemsSelex Sensors and Airborne System
Direct Differential Photometric Stereo Shape Recovery of Diffuse and Specular Surfaces
This is the author accepted manuscript. The final version is available from Springer via http://dx.doi.org/10.1007/s10851-016-0633-0Recovering the 3D shape of an object from shading is a challenging problem due to the complexity of modeling light propagation and surface reflections. Photometric Stereo (PS) is broadly considered a suitable approach for high-resolution shape recovery, but its functionality is restricted to a limited set of object surfaces and controlled lighting setup. In particular, PS models generally consider reflection from objects as purely diffuse, with specularities being regarded as a nuisance that breaks down shape reconstruction. This is a serious drawback for implementing PS approaches, since most common materials have prominent specular components. In this paper, we propose a PS model that solves the problem for both diffuse and specular components aimed at shape recovery of generic objects with the approach being independent of the albedo values thanks to the image ratio formulation used. Notably, we show that by including specularities, it is possible to solve the PS problem for a minimal number of three images using a setup with three calibrated lights and a standard industrial camera. Even if an initial separation of diffuse and specular components is still required for each input image, experimental results on synthetic and real objects demonstrate the feasibility of our approach for shape reconstruction of complex geometries.The first author acknowledges the support of INDAM under the GNCS research Project âMetodi numerici per la regolarizzazione nella ricostruzione feature-preserving di dati.
Photometric stereo with only two images: A theoretical study and numerical resolution
This work tackles the problem of two-image photometric stereo. This problem constitutes the intermediate case between conventional photometric stereo with at least three images, which is well-posed, and shape-from-shading, which is ill-posed. We first provide a theoretical study of ambiguities arising in this intermediate case. Based on this study, we show that when the albedo is known, disambiguation can be formulated as a binary labeling problem, using integrability and a nonstationary Ising model. The resulting optimization problem is solved efficiently by resorting to the graph cut algorithm. These theoretical and numerical contributions are eventually validated in an application to three-image photometric stereo with shadows.Roberto Mecca was a Marie Curie Fellow of the Instituto Nazionale di Alta Matematic
- âŠ