Surface reconstruction with higher-order smoothness

This work proposes a method to reconstruct surfaces with higher-order smoothness from noisy 3D measurements. The reconstructed surface is implicitly represented by the zero-level set of a continuous valued embedding function. The key idea is to find a function whose higher-order derivatives are regularized and whose gradient is best aligned with a vector field defined by the input point set. In contrast to methods based on the first-order variation of the function that are biased toward the constant functions and treat the extraction of the isosurface without aliasing artifacts as an afterthought, we impose a higher-order smoothness directly on the embedding function. After solving a convex optimization problem with a multiscale iterative scheme, a triangulated surface can be extracted using the marching cubes algorithm. We demonstrated the proposed method on several data sets obtained from raw laser-scanners and multiview stereo approaches. Experimental results confirm that our approach allows us to reconstruct smooth surfaces from points in the presence of noise, outliers, large missing parts, and very coarse orientation information.     

Optimal Reconstruction of Approximate Planar Surfaces Using Photometric Stereo

Photometric stereo can be used to obtain a fast and noncontact surface reconstruction of Lambertian surfaces. Despite several published works concerning the uncertainties and optimal light configurations of photometric stereo, no solutions for optimal surface reconstruction from noisy real images have been proposed. In this paper, optimal surface reconstruction methods for approximate planar textured surfaces using photometric stereo are derived, given that the statistics of imaging errors are measurable. Simulated and real surfaces are experimentally studied, and the results validate that the proposed approaches improve the surface reconstruction especially for the high-frequency height variations.     

Photometric stereo with an arbitrary number of illuminants

We present an optimal generalisation of the 4-light photometric stereo technique for an arbitrary number of Q illuminants. We assume that the surface reflectance can be approximated by the Lambertian model plus a specular reflection. The algorithm works in a recursive manner eliminating the pixel intensities affected by shadows or highlights, based on a least squares error technique, retaining only the information coming from illumination directions that can be used for photometric stereo reconstruction of the normal of the corresponding surface patch. We report results for both simulated and real surfaces and compare them with the results of other state of the art photometric stereo algorithms.     

Stereo hidden Markov modeling for noise robust speech recognition

This paper investigates a noise robust technique for automatic speech recognition which exploits hidden Markov modeling of stereo speech features from clean and noisy channels. The HMM trained this way, referred to as stereo HMM, has in each state a Gaussian mixture model (GMM) with a joint distribution of both clean and noisy speech features. Given the noisy speech input, the stereo HMM gives rise to a two-pass compensation and decoding process where MMSE denoising based on N-best hypotheses is first performed and followed by decoding the denoised speech in a reduced search space on lattice. Compared to the feature space GMM-based denoising approaches, the stereo HMM is advantageous as it has finer-grained noise compensation and makes use of information of the whole noisy feature sequence for the prediction of each individual clean feature. Experiments on large vocabulary spontaneous speech from speech-to-speech translation applications show that the proposed technique yields superior performance than its feature space counterpart in noisy conditions while still maintaining decent performance in clean conditions.     

Stereo Image Analysis of Non-Lambertian Surfaces

Stereo image analysis is based on establishing correspondences between a pair of images by determining similarity measures for potentially corresponding image parts. Such similarity criteria are only strictly valid for surfaces with Lambertian (diffuse) reflectance characteristics. Specular reflections are viewpoint dependent and may thus cause large intensity differences at corresponding image points. In the presence of specular reflections, traditional stereo approaches are often unable to establish correspondences at all, or the inferred disparity values tend to be inaccurate, or the established correspondences do not belong to the same physical surface point. The stereo image analysis framework for non-Lambertian surfaces presented in this contribution combines geometric cues with photometric and polarimetric information into an iterative scheme that allows to establish stereo correspondences in accordance with the specular reflectance behaviour and at the same time to determine the surface gradient field based on the known photometric and polarimetric reflectance properties. The described approach yields a dense 3D reconstruction of the surface which is consistent with all observed geometric and photopolarimetric data. Initially, a sparse 3D point cloud of the surface is computed by traditional blockmatching stereo. Subsequently, a dense 3D profile of the surface is determined in the coordinate system of camera 1 based on the shape from photopolarimetric reflectance and depth technique. A synthetic image of the surface is rendered in the coordinate system of camera 2 using the illumination direction and reflectance properties of the surface material. Point correspondences between the rendered image and the observed image of camera 2 are established with the blockmatching technique. This procedure yields an increased number of 3D points of higher accuracy, compared to the initial 3D point cloud. The improved 3D point cloud is used to compute a refined dense 3D surface profile. These steps are iterated until convergence of the 3D reconstruction. An experimental evaluation of our method is provided for areas of several square centimetres of forged and cast iron objects with rough surfaces displaying both diffuse and significant specular reflectance components, where traditional stereo image analysis largely fails. A comparison to independently measured ground truth data reveals that the root-mean-square error of the 3D reconstruction results is typically of the order 30–100 μm at a lateral pixel resolution of 86 μm. For two example surfaces, the number of stereo correspondences established by the specular stereo algorithm is several orders of magnitude higher than the initial number of 3D points. For one example surface, the number of stereo correspondences decreases by a factor of about two, but the 3D point cloud obtained with the specular stereo method is less noisy, contains a negligible number of outliers, and shows significantly more surface detail than the initial 3D point cloud. For poorly known reflectance parameters we observe a graceful degradation of the accuracy of 3D reconstruction.     

一种鲁棒的基于光度立体视觉的表面重建方法

提出一种基于先进的凸优化技术的光度立体视觉重建框架. 首先通过鲁棒的主成分分析(Robust principle component analysis, RPCA)祛除图像噪声, 得到低秩矩阵和物体表面向量场, 然后再通过表面重建算法从向量场来恢复物体形状. 相对于先前的一些使用最小二乘或者一些启发式鲁棒技术的方法, 该方法使用了所有可用的信息, 可以同时修复数据中的丢失和噪声数据, 显示出了较高的计算效率以及对于大的稀疏噪声的鲁棒性. 实验结果表明, 本文提出的框架大大提高了在噪声存在情况下物体表面的重建精度.     

Reconstructing surfaces by volumetric regularization using radial basis functions

We present a new method of surface reconstruction that generates smooth and seamless models from sparse, noisy, nonuniform, and low resolution range data. Data acquisition techniques from computer vision, such as stereo range images and space carving, produce 3D point sets that are imprecise and nonuniform when compared to laser or optical range scanners. Traditional reconstruction algorithms designed for dense and precise data do not produce smooth reconstructions when applied to vision-based data sets. Our method constructs a 3D implicit surface, formulated as a sum of weighted radial basis functions. We achieve three primary advantages over existing algorithms: (1) the implicit functions we construct estimate the surface well in regions where there is little data, (2) the reconstructed surface is insensitive to noise in data acquisition because we can allow the surface to approximate, rather than exactly interpolate, the data, and (3) the reconstructed surface is locally detailed, yet globally smooth, because we use radial basis functions that achieve multiple orders of smoothness.     

Joint Estimation of Shape and Reflectance using Multiple Images with Known Illumination Conditions

We propose a generative model based method for recovering both the shape and the reflectance of the surface(s) of a scene from multiple images, assuming that illumination conditions and cameras calibration are known in advance. Based on a variational framework and via gradient descents, the algorithm minimizes simultaneously and consistently a global cost functional with respect to both shape and reflectance. The motivations for our approach are threefold. (1) Contrary to previous works which mainly consider specific individual scenarios, our method applies indiscriminately to a number of classical scenarios; in particular it works for classical stereovision, multiview photometric stereo and multiview shape from shading. It works with changing as well as static illumination. (2) Our approach naturally combines stereo, silhouette and shading cues in a single framework. (3) Moreover, unlike most previous methods dealing with only Lambertian surfaces, the proposed method considers general dichromatic surfaces. We verify the method using various synthetic and real data sets.     

LED-Based Photometric Stereo: Modeling,Calibration and Numerical Solution

We conduct a thorough study of photometric stereo under nearby point light source illumination, from modeling to numerical solution, through calibration. In the classical formulation of photometric stereo, the luminous fluxes are assumed to be directional, which is very difficult to achieve in practice. Rather, we use light-emitting diodes to illuminate the scene to be reconstructed. Such point light sources are very convenient to use, yet they yield a more complex photometric stereo model which is arduous to solve. We first derive in a physically sound manner this model, and show how to calibrate its parameters. Then, we discuss two state-of-the-art numerical solutions. The first one alternatingly estimates the albedo and the normals, and then integrates the normals into a depth map. It is shown empirically to be independent from the initialization, but convergence of this sequential approach is not established. The second one directly recovers the depth, by formulating photometric stereo as a system of nonlinear partial differential equations (PDEs), which are linearized using image ratios. Although the sequential approach is avoided, initialization matters a lot and convergence is not established either. Therefore, we introduce a provably convergent alternating reweighted least-squares scheme for solving the original system of nonlinear PDEs. Finally, we extend this study to the case of RGB images.     

Translational photometric alignment of single-view image sequences

Photometric stereo is a well-established method to estimate surface normals of an object. When coupled with depth-map estimation, it can be used to reconstruct an object’s height field. Typically, photometric stereo requires an image sequence of an object under the same viewpoint but with differing illumination directions. One crucial assumption of this configuration is perfect pixel correspondence across images in the sequence. While this assumption is often satisfied, certain setups are susceptible to translational errors or misalignments across images. Current methods to align image sequences were not designed specifically for single-view photometric stereo. Thus, they either struggle to account for changing illumination across images, require training sets, or are overly complex for these conditions. However, the unique nature of single-view photometric stereo allows one to model misaligned image sequences using the underlying image formation model and a set of translational shifts. This paper introduces such a technique, entitled translational photometric alignment, that employs the Lambertian model of image formation. This reduces the alignment problem to minimizing a nonlinear sum-squared error function in order to best reconcile the observed images with the generative model. Thus, the end goal of translational photometric alignment is not only to align image sequences, but also to produce the best surface-normal estimates given the observed images. Controlled experiments on the Yale Face Database B demonstrate the high accuracy of translational photometric alignment. The utility and benefits of the technique are further illustrated by additional experiments on image sequences suffering from uncontrolled real-world misalignments.     

一种基于梯度的健壮的指纹方向场估计算法

作为指纹的全局特征,指纹方向场在自动指纹识别系统中发挥了非常重要的作用.提出了一种基于梯度的健壮的指纹方向场估计算法,新算法首先归一化点梯度向量并计算块梯度向量及相应的块一致性;然后估计噪声区域;最后采用基于迭代的方法,重新估计所有块梯度向量并将梯度向量场转化为方向场.实验结果表明,与已有基于梯度的指纹方向场估计算法相比,新算法具有更高的准确性及抗噪性能,并能较好地估计大块噪声内的方向场,是一种较为健壮的指纹方向场估计算法.     

Photometric Stereo with General,Unknown Lighting

Work on photometric stereo has shown how to recover the shape and reflectance properties of an object using multiple images taken with a fixed viewpoint and variable lighting conditions. This work has primarily relied on known lighting conditions or the presence of a single point source of light in each image. In this paper we show how to perform photometric stereo assuming that all lights in a scene are distant from the object but otherwise unconstrained. Lighting in each image may be an unknown and may include arbitrary combination of diffuse, point and extended sources. Our work is based on recent results showing that for Lambertian objects, general lighting conditions can be represented using low order spherical harmonics. Using this representation we can recover shape by performing a simple optimization in a low-dimensional space. We also analyze the shape ambiguities that arise in such a representation. We demonstrate our method by reconstructing the shape of objects from images obtained under a variety of lightings. We further compare the reconstructed shapes against shapes obtained with a laser scanner.     

Nonlinearities and Noise Reduction in 3-Source Photometric Stereo

1-D Leap-Frog (L. Noakes, J. Math. Australian Soc. A, Vol. 64, pp. 37–50, 1999) is an iterative scheme for solving a class of nonquadratic optimization problems. In this paper a 2-D version of Leap-Frog is applied to a non optimization problem in computer vision, namely the recovery (so far as possible) of an unknown surface from 3 noisy camera images. This contrasts with previous work on photometric stereo, in which noise is added to the gradient of the height function rather than camera images. Given a suitable initial guess, 2-D Leap-Frog is proved to converge to the maximum-likelihood estimate for the vision problem. Performance is illustrated by examples.     

A phase-field approach for minimizing the area of triply periodic surfaces with volume constraint

In this paper, we present an accurate and efficient algorithm to generate constant mean curvature surfaces with volume constraint using a phase-field model. We implement our proposed algorithm using an unconditionally gradient stable nonlinear splitting scheme. Starting from the periodic nodal surface approximation to minimal surfaces, we can generate various constant mean curvature surfaces with given volume fractions. We generate and study the Schwarz primitive (P), Schwarz diamond (D), and Schoen gyroid (G) surfaces with various volume fractions. This technique for generating constant mean curvature surfaces can be used to design biomedical scaffolds with optimal mechanical and biomorphic properties.     

The 4-source photometric stereo technique for three-dimensional surfaces in the presence of highlights and shadows

We present an algorithm for separating the local gradient information and Lambertian color by using 4-source color photometric stereo in the presence of highlights and shadows. We assume that the surface reflectance can be approximated by the sum of a Lambertian and a specular component. The conventional photometric method is generalized for color images. Shadows and highlights in the input images are detected using either spectral or directional cues and excluded from the recovery process, thus giving more reliable estimates of local surface parameters.     

Multiview photometric stereo

This paper addresses the problem of obtaining complete, detailed reconstructions of textureless shiny objects. We present an algorithm which uses silhouettes of the object, as well as images obtained under changing illumination conditions. In contrast with previous photometric stereo techniques, ours is not limited to a single viewpoint but produces accurate reconstructions in full 3D. A number of images of the object are obtained from multiple viewpoints, under varying lighting conditions. Starting from the silhouettes, the algorithm recovers camera motion and constructs the object's visual hull. This is then used to recover the illumination and initialise a multi-view photometric stereo scheme to obtain a closed surface reconstruction. There are two main contributions in this paper: Firstly we describe a robust technique to estimate light directions and intensities and secondly, we introduce a novel formulation of photometric stereo which combines multiple viewpoints and hence allows closed surface reconstructions. The algorithm has been implemented as a practical model acquisition system. Here, a quantitative evaluation of the algorithm on synthetic data is presented together with complete reconstructions of challenging real objects. Finally, we show experimentally how even in the case of highly textured objects, this technique can greatly improve on correspondence-based multi-view stereo results.     

基于分层视差估计的立体图象编码

基于立体视频数据压缩的目的，提出了一种基于分层视差估计/补偿的立体图象编码方案。该方案是采用JPEG标准独立编码参数图象，并利用视差估计/补偿技术编码目标图象，应用分层马尔可夫随机场（MRF）模型。率失真（RD）模型以及交叠块匹配的混合视差估计/补偿算法，可得到光滑准确的视差场，与通常的变尺寸块匹配（VSBM）相比，该算法得到的视差补偿图象的峰值信噪比（PSNR）可提高2.5dB左右；双向半像素精度的视差估计/补偿的性能要比单向整像素搜索提高3dB，实验结果表明，该立体图象编码方案能有效地压缩立体图象数据，并可推广到立体序列图象的编码压缩中。     

Implicit Surface-Based Geometric Fusion

This paper introduces a general purpose algorithm for reliable integration of sets of surface measurements into a single 3D model. The new algorithm constructs a single continuous implicit surface representation which is the zero-set of a scalar field function. An explicit object model is obtained using any implicit surface polygonization algorithm. Object models are reconstructed from both multiple view conventional 2.5D range images and hand-held sensor range data. To our knowledge this is the first geometric fusion algorithm capable of reconstructing 3D object models from noisy hand-held sensor range data.This approach has several important advantages over existing techniques. The implicit surface representation allows reconstruction of unknown objects of arbitrary topology and geometry. A continuous implicit surface representation enables reliable reconstruction of complex geometry. Correct integration of overlapping surface measurements in the presence of noise is achieved using geometric constraints based on measurement uncertainty. The use of measurement uncertainty ensures that the algorithm is robust to significant levels of measurement noise. Previous implicit surface-based approaches use discrete representations resulting in unreliable reconstruction for regions of high curvature or thin surface sections. Direct representation of the implicit surface boundary ensures correct reconstruction of arbitrary topology object surfaces. Fusion of overlapping measurements is performed using operations in 3D space only. This avoids the local 2D projection required for many previous methods which results in limitations on the object surface geometry that is reliably reconstructed. All previous geometric fusion algorithms developed for conventional range sensor data are based on the 2.5D image structure preventing their use for hand-held sensor data. Performance evaluation of the new integration algorithm against existing techniques demonstrates improved reconstruction of complex geometry.     

Efficient surface reconstruction using generalized coulomb potentials

We propose a novel, geometrically adaptive method for surface reconstruction from noisy and sparse point clouds, without orientation information. The method employs a fast convection algorithm to attract the evolving surface towards the data points. The force field in which the surface is convected is based on generalized Coulomb potentials evaluated on an adaptive grid (i.e., an octree) using a fast, hierarchical algorithm. Formulating reconstruction as a convection problem in a velocity field generated by Coulomb potentials offers a number of advantages. Unlike methods which compute the distance from the data set to the implicit surface, which are sensitive to noise due to the very reliance on the distance transform, our method is highly resilient to shot noise since global, generalized Coulomb potentials can be used to disregard the presence of outliers due to noise. Coulomb potentials represent long-range interactions that consider all data points at once, and thus they convey global information which is crucial in the fitting process. Both the spatial and temporal complexities of our spatially-adaptive method are proportional to the size of the reconstructed object, which makes our method compare favorably with respect to previous approaches in terms of speed and flexibility. Experiments with sparse as well as noisy data sets show that the method is capable of delivering crisp and detailed yet smooth surfaces.