9 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
A fast 3D reconstruction system with a low-cost camera accessory
Photometric stereo is a three dimensional (3D) imaging technique that uses multiple 2D images, obtained from a fixed camera perspective, with different illumination directions. Compared to other 3D imaging methods such as geometry modeling and 3D-scanning, it comes with a number of advantages, such as having a simple and efficient reconstruction routine. In this work, we describe a low-cost accessory to a commercial digital single-lens reflex (DSLR) camera system allowing fast reconstruction of 3D objects using photometric stereo. The accessory consists of four white LED lights fixed to the lens of a commercial DSLR camera and a USB programmable controller board to sequentially control the illumination. 3D images are derived for different objects with varying geometric complexity and results are presented, showing a typical height error of <3 mm for a 50 mm sized object
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
Multi-View Azimuth Stereo via Tangent Space Consistency
We present a method for 3D reconstruction only using calibrated multi-view
surface azimuth maps. Our method, multi-view azimuth stereo, is effective for
textureless or specular surfaces, which are difficult for conventional
multi-view stereo methods. We introduce the concept of tangent space
consistency: Multi-view azimuth observations of a surface point should be
lifted to the same tangent space. Leveraging this consistency, we recover the
shape by optimizing a neural implicit surface representation. Our method
harnesses the robust azimuth estimation capabilities of photometric stereo
methods or polarization imaging while bypassing potentially complex zenith
angle estimation. Experiments using azimuth maps from various sources validate
the accurate shape recovery with our method, even without zenith angles.Comment: CVPR 2023 camera-ready. Appendices after references. 16 pages, 20
figures. Project page: https://xucao-42.github.io/mvas_homepage
Robust Algorithms for Low-Rank and Sparse Matrix Models
Data in statistical signal processing problems is often inherently matrix-valued, and a natural first step in working with such data is to impose a model with structure that captures the distinctive features of the underlying data. Under the right model, one can design algorithms that can reliably tease weak signals out of highly corrupted data. In this thesis, we study two important classes of matrix structure: low-rankness and sparsity. In particular, we focus on robust principal component analysis (PCA) models that decompose data into the sum of low-rank and sparse (in an appropriate sense) components. Robust PCA models are popular because they are useful models for data in practice and because efficient algorithms exist for solving them.
This thesis focuses on developing new robust PCA algorithms that advance the state-of-the-art in several key respects. First, we develop a theoretical understanding of the effect of outliers on PCA and the extent to which one can reliably reject outliers from corrupted data using thresholding schemes. We apply these insights and other recent results from low-rank matrix estimation to design robust PCA algorithms with improved low-rank models that are well-suited for processing highly corrupted data. On the sparse modeling front, we use sparse signal models like spatial continuity and dictionary learning to develop new methods with important adaptive representational capabilities. We also propose efficient algorithms for implementing our methods, including an extension of our dictionary learning algorithms to the online or sequential data setting. The underlying theme of our work is to combine ideas from low-rank and sparse modeling in novel ways to design robust algorithms that produce accurate reconstructions from highly undersampled or corrupted data. We consider a variety of application domains for our methods, including foreground-background separation, photometric stereo, and inverse problems such as video inpainting and dynamic magnetic resonance imaging.PHDElectrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/143925/1/brimoor_1.pd