We present an efficient deterministic hypothesis generation algorithm for robust fitting of multiple structures based on the maximum feasible subsystem (MaxFS) framework. Despite its advantage, a global optimization method such as MaxFS has two main limitations for geometric model fitting. First, its performance is much influenced by the user-specified inlier scale. Second, it is computationally inefficient for large data. The presented algorithm, called iterative MaxFS with inlier scale (IMaxFS-ISE), iteratively estimates model parameters and inlier scale and also overcomes the second limitation by reducing data for the MaxFS problem. The IMaxFS-ISE algorithm generates hypotheses only with top-n ranked subsets based on matching scores and data fitting residuals. This reduction of data for the MaxFS problem makes the algorithm computationally realistic. A sequential "fitting-and-removing" procedure is repeated until overall energy function does not decrease. Experimental results demonstrate that our method can generate more reliable and consistent hypotheses than random sampling-based methods for estimating multiple structures from data with many outliers.

This paper presents a global minimization framework for estimating analytical BRDF model parameters using the techniques of convex programming and branch and bound. Traditional local minimization suffers from local minima and requires a large number of initial conditions and supervision for successful results especially when a model is highly complex and nonlinear. We consider the Cook-Torrance model, a parametric model with the Gaussian-like Beckmann distributions for specular reflectances. Instead of optimizing the multiple parameters simultaneously, we search over all possible surface roughness values based on a branch-and-bound algorithm, and reduce the estimation problem to convex minimization with known fixed surface roughness. Our algorithm guarantees globally optimal solutions. Experiments have been carried out for isotropic surfaces to validate the method using the extensive high-precision measurements from the MERL BRDF database.

We propose a branch-and-bound algorithm to obtain the globally optimal relative rotation between a camera and the rotation sensor attached to it. Compared to previous methods, our approach directly minimizes the image space error related to the measurements which is very natural for camera-based systems. Our algorithm is based on the observation that we may evaluate the residual when the rotation matrix is known. We propose a feasibility test algorithm for the branch-and-bound to efficiently reduce the search volume of the rotation domain. Experimental results are provided using synthetic and real data sets.

Missing data are common in range images, due to geometric occlusions, limitations in the sensor field of view, poor reflectivity, depth discontinuities, and cast shadows. Using registration to align these data often fails, because points without valid correspondences can be incorrectly matched. This paper presents a maximum likelihood method for registration of scenes with unmatched or missing data. Using ray casting, correspondences are formed between valid and missing points in each view. These correspondences are used to classify points by their visibility properties, including occlusions, field of view, and shadow regions. The likelihood of each point match is then determined using statistical properties of the sensor, such as noise and outlier distributions. Experiments demonstrate a high rates of convergence on complex scenes with varying degrees of overlap.

This paper investigates the use of photometric features for the pair-wise registration of range images. Many artificial and natural objects exhibit abundant surface texture that may not be revealed in range data, and most structured light and laser range sensors are capable of capturing either grayscale or color photometric intensity in addition to range data. Nevertheless, the use of photometric features has not been widely investigated for range data registration, despite widespread research into local feature descriptors for object recognition in 2D photometric images. This paper addresses some of the problems that arise in using photometric features for range data registration, and presents a systematic method for their use. Potentially useful photometric features are detected on planar regions in 3D, and then reprojected to 2D to remove the perspective distortion. Then, a well-established 2D rotation- and brightness-invariant image feature descriptor is used for matching. Range data alignment is performed using a RANSAC algorithm, with verification performed in 3D. Experimental results demonstrate the effectiveness of this method.

Abstract Mesh simplification is the process of reducing the number of triangles in a mesh representation of object surface. For a given level of detail or error tolerance, the conventional mesh simplification algorithms maximize the edge length globally, without explicitly considering local object shape. In this paper, we present a shape‐adaptive mesh simplification algorithm that locally maximizes edge length, depending on local shape. The proposed algorithm achieves shape‐adaptive simplification by iteratively maximizing edges between vertices, based on comparison with the ‘optimal’ edge lengths derived from local directional curvatures for a given error tolerance. Edge‐based processing facilitates the local shape adaptation and preserves sharp features. Experimental results demonstrate the efficacy of the proposed algorithm, by showing good visual quality and extremely small approximation error. Copyright © 2003 John Wiley & Sons, Ltd.

Mesh simplification is the process of reducing the number of triangles in a mesh representation of object surface. For a given level of detail or error tolerance, the conventional mesh simplification algorithms maximize the edge length globally, without explicitly considering the local object shape. In this paper we present a shape-adaptive mesh simplification algorithm that locally maximizes the edge length, depending on the local shape. The proposed algorithm achieves shape-adaptive simplification by iteratively maximizing edges between vertices, based on a comparison with the "optimal" edge lengths derived from local directional curvatures for a given error tolerance.

Investigates the use of Euclidean invariant features in a generalization of iterative closest point (ICP) registration of range images. Pointwise correspondences are chosen as the closest point with respect to a weighted linear combination of positional and feature distances. It is shown that, under ideal noise-free conditions, correspondences formed using this distance function are correct more often than correspondences formed using the positional distance alone. In addition, monotonic convergence to at least a local minimum is shown to hold for this method. When noise is present, a method that automatically sets the optimal relative contribution of features and positions is described. This method trades off the error in feature values due to noise against the error in positions due to misalignment. Experimental results suggest that using invariant features decreases the probability of being trapped in a local minimum and may be an effective solution for difficult range image registration problems where the scene is very small compared to the model.

Spectral Spatial Gradients (SSGs) have been suggested as features invariant to illumination variation for color-based recognition and indexing. While SSGs have a greater degree of invariance than Spectral Gradients (SGs), they may have a reduced discrimination power between objects since they use only spatial changes of object reflectance. The approach presented is to use the framework of SGs and SSGs to create a recognition method which is invariant to varying illumination without discarding the reflectance distribution information. Two techniques are used to extract the varying illumination. The first is to assume that low-frequency SG variation is due to illumination. The second method uses regions with matching SSGs to get local estimates of illumination. Once the local illumination variation has been extracted, its effect on the SGs can be removed and the resulting Adapted Spectral Gradients (ASGs) have a greater power of discrimination for some objects than SSG features. Experimental results demonstrate cases where ASGs show improved performance.

To construct three dimensional models from range data, the simultaneous registration of multiple views must be accomplished. There exists a natural hierarchy between the local problem of aligning two views and the global problem of maintaining a consistent network of relative orientation and positions between views. Our paper addresses the global problem, where we compute orientation and position estimates from noisy inter-frame measurements. This is accomplished by building a graph of infer-frame relations, selecting a set of basis cycles which fully describe the graph, and distributing accumulated error about the basis cycles.

Variability in object appearance due to illumination conditions has typically been modelled for only diffuse reflection. In this paper we present a method for determining multiple reflection components for a set of photometric images, and describe a linear representation of these reflection elements for enumerating the possible illumination appearances of an object. The proposed approach involves a simultaneous estimation of reflectance parameters that can be generalized to yield a separation for an arbitrary number of reflection components. We show that the separated components of photometric images can be combined to form their counterparts in images with different illumination. Results are presented to illustrate the performance of this method for uncalibrated lighting directions.

The light reflected from a surface depends on the scene geometry, the incident illumination and the surface material. A novel methodology is presented which extracts reflectivity information of the various materials in the scene independent of incident light and scene geometry. A scene is captured under different narrow-band color filters and the spectral derivatives of the scene are computed. The resulting spectral derivatives form a spectral gradient at each pixel. This spectral gradient is a material descriptor which is invariant to scene geometry and incident illumination for smooth diffuse surfaces. Spectral gradients can discriminate among smooth dielectrics with different reflectance properties independent of viewing conditions.

The appearance of an object can vary considerably with changes in illumination conditions. Methods have been developed to describe these differences for diffuse reflection using the Lambertian model, but little work has been done in characterizing specular appearance. Towards a more comprehensive global reflectance descriptor, this paper focuses on a representation of specular appearance based on an approximate specular reflection model derived from Torrance-Sparrow. We propose that under certain illumination and surface conditions local specular structure can be expressed by the logarithms of three intensity-normalized photometric images. The total number of photometric images needed for representing global specular appearance depends on the object surface roughness, and we suggest an illumination planning method for determining the number of images. Experimental results demonstrate the effectiveness of this logarithmic model as a specular descriptor.

To account for the variability of object appearance due to differences in illumination, attention has recently been focused on representing the set of images for all possible lighting conditions. Approaches that address this problem have primarily focused on lighting differences for diffuse reflection using the Lambertian model; however specular reflections can additionally present considerable disparity in appearance. We present a method for representing illumination appearance for both diffuse and specular reflections for objects of uniform surface roughness using four photometric images. This approach uses separation of reflection components, extracts surface reflectances and roughness, and produces arbitrary lighting images without explicit computation of surface shape. Experimental results demonstrate the validity of the proposed method for constructing diffuse and specular appearances.

Investigates the use of Euclidean invariants in the iterative closest point registration of range images. Invariants are used in a modified distance function for the selection of point correspondences. Theoretical results show that under ideal conditions, using invariants can only improve the chance of a making correct correspondences. In addition, monotonic convergence to a local minimum is preserved. Experimental results show that using invariant features accelerates the registration and decreases the probability of being trapped in a local minimum.

Most of the recent color recognition/indexing approaches concentrate on establishing invariance to illumination color to improve the utility of color recognition. However, other effects caused by illumination pose and specularity on three-dimensional object surfaces have not received notable attention. We present a chromaticity recognition method that discounts the effects of illumination pose, illumination color and specularity. It utilizes a chromaticity space based on log-ratio of sensor responses for illumination pose and color invariance. A model-based specularity detection/rejection algorithm can be used to improve the chromaticity recognition and illumination estimation for objects including specular reflections.

The distribution of object colors can be effectively utilized for recognition and indexing. Difficulties arise in the recognition of object color distributions when there are variations in illumination color changes in object pose with respect to illumination direction, and specular reflections. However, most of the recent approaches to color-based recognition focus mainly on illumination color invariance. The authors propose an approach that identifies object color distributions influenced by: (1) illumination pose, (2) illumination color and (3) specularity. They suggest the use of chromaticity distributions to achieve illumination pose invariance. To characterize changes in chromaticity distribution due to illumination color a set of chromaticity histograms of each object is generated for a range of lighting colors based on linear models of illumination and reflectance, and the histograms are represented using a small number of eigenbasis vectors constructed from principal components analysis. Since specular reflections may alter the chromaticity distributions of rest objects, a model-based specularity detection/rejection algorithm, called chromaticity differencing, is developed to reduce these effects.

We propose a specularity detection method based on a synergistic integration of color and polarization information from multiple views. The presence of specularity in images can cause many traditional computer vision processes to produce misleading results. Recent physics-based direction methods have provided much success in locating specularity; however no single cue reveals the full structure of specular reflections. Our method merges multiple-view color and polarization, two physically independent but highly effective cues, in a way that they mutually benefit from each other's strengths. In a fused color and polarization space, the proposed algorithm compares the distributions of sensor data from multiple views for detection of specular. We show that the efficacy of this new cue extends beyond that of the sum of its parts, and confirming experimental results are presented.

A computational model for color image segmentation is proposed based on the physical properties of sensors, illumination lights, and surface reflectances. For image segmentation to depend only on the change of material surface, variations of surface reflection due to illumination, shading, shadows, and highlights should be discounted from a measured image. The authors use the dichromatic model for dielectric materials and develop a metric space of intensity, hue, and saturation in order to interpret various light-surface interactions better. Using the established model for surface reflection, the authors perform color image segmentation based on the material change with detection of highlights and small interreflections between adjacent objects. A reference plate is used to whiten global illumination. The detected interreflections represent local variation of illumination.>