Robustly registering range images using local distribution of albedo

https://doi.org/10.1016/j.cviu.2010.11.016Get rights and content

Abstract

We propose a robust method for registering overlapping range images of a Lambertian object under a rough estimate of illumination. Because reflectance properties are invariant to changes in illumination, the albedo is promising to range image registration of Lambertian objects lacking in discriminative geometric features under variable illumination. We use adaptive regions in our method to model the local distribution of albedo, which enables us to stably extract the reliable attributes of each point against illumination estimates. We use a level-set method to grow robust and adaptive regions to define these attributes. A similarity metric between two attributes is also defined to match points in the overlapping area. Moreover, remaining mismatches are efficiently removed using the rigidity constraint of surfaces. Our experiments using synthetic and real data demonstrate the robustness and effectiveness of our proposed method.

Research highlights

► Registering range images of Lambertian objects using albedo. ► Matching corresponding points using local distribution of albedo. ► Modeling local distribution of albedo using adaptive regions. ► Eliminating mismatches using the rigidity constraint of surfaces.

Introduction

The 3D modeling process of real objects has attracted increased interest during the past decade for applications in augmented reality, cinema, computer games, or medicine. Because it is labour intensive to create a detailed 3D model of a real object using various modeling software, automating the whole modeling process has attracted considerable interest in recent years. This process can be divided into five steps: (1) data acquisition, (2) reconstruction of 3D images, (3) 3D registration, (4) merging, and (5) inverse rendering.

Recent acquisition devices, like modern laser range scanners, can retrieve both the 3D shape and color image of an object from a fixed viewpoint; the acquired 3D image in this case is called a range image (Fig. 1). Therefore the second step of the 3D modeling process can be omitted for range images. However, as some parts of an object are occluded from a fixed viewpoint, multiple viewpoints are required to obtain the full 3D shape of the object. Therefore, 3D images of partially overlapping parts of the object, acquired from different viewpoints have to be aligned. This process is called 3D registration. There are two categories for 3D registration. The first, called coarse registration, is to find rough alignment between two 3D images, starting from sufficiently different poses [1]. The second, called fine registration, is to find accurate alignment between two 3D images, starting from rough alignment. We refer to range image registration when using range images [2].

The most common approach to registering range images is to find correspondences in points between two overlapping range images and then accordingly estimate the transformation in aligning the two range images. Several methods for registering range images can be found in the literature that use geometric features for computing correspondences in points. However, we assume that the range images to be registered have simple textured shapes (like cylinders) and are thus devoid of salient geometric features. Consequently, photometric features in addition to geometric features are required to compute correspondences in points.

Reflectance properties as a photometric feature are promising because of their independence of the pose of the object relative to the sensor. Retrieving these properties has provided a major research area in physics-based vision called reflectance from brightness (with a known shape and illumination). Cerman et al. [3] recently proposed a method, which we call ICP using albedo (ICPA), using the reflectance properties (which is the albedo for Lambertian objects) of the object surface in the standard iterative closest point (ICP) process. The illumination conditions have to be precisely known a priori so that the reflectance of the surface of an object can be accurately retrieved from its shape and brightness. Consequently, the direct use of albedo values as a matching constraint, as achieved by ICPA, requires global illumination to be accurately estimated, which is difficult to attain in practice under real illumination conditions.

We introduce a region-based approach to using reflectance attributes, namely the albedo, for robust fine registration of Lambertian objects under rough estimates of illumination. Because retrieving the albedo on the surface of a Lambertian object is sensitive to estimates of illumination, the albedo of a point cannot be directly used under rough estimates of illumination. We thus employ the local distribution of albedo for registration. Our proposed method uses adaptive regions to model the local distribution of albedo on the object surface, which leads to robust extraction of attributes against illumination estimates. These regions are grown using a level-set method, allowing us to exclude outliers and then to define more reliable attributes. We define a robust metric, using the principal component analysis (PCA) of each region to find correspondences in points. This is a stable and powerful metric to maximize the number of correct matches, even under rough estimates of illumination. Moreover, we reject remaining mismatches by enforcing the rigidity constraint on surfaces and then estimate transformation using the weighted least squares (WLS) method. Our method has advantages with rough estimates of illumination and with large amounts of noise. These advantages allow us to use simple models of illumination to register range images. Our experiments using synthetic and real data demonstrate that our method is robust. We assume in this paper that the surfaces’ textures present sufficient saliency to constrain the matching of two overlapping range images. We do not consider uniform nor ‘salt and pepper’ textures, nor repetitive patterns. We also assume that the objects do not present self-occlusions, shadows nor interreflections.

Section snippets

Related work

During the past few decades, many approaches to registering range images have been discussed. The most well-known approach to fine registration is the iterative closest point (ICP) [4], [5]. This method iterates two steps: it matches each point of the first range image with its closest point on the other range image, and estimates the transformation between the two range images using the correspondences in the matched points. The ICP converges monotonically to a local minimum and therefore

Proposed method

Our proposed method uses the local distribution of albedo on the surface to define discriminative attributes that are robust to data noise. We define a similarity metric to efficiently match points in the overlapping part of two range images and use the rigidity constraint of surfaces to refine matching. The transformation aligning two range images is then computed using the WLS approach.

Computational complexity analysis

Our proposed algorithm has its input of two range images with N points and outputs the rigid transformation aligning the two range images. Here we briefly give analysis on the computational complexity to our proposed algorithm. We refer to Fig. 2 for the different steps of our method and give the computational complexity for each of these steps.

The first part of our proposed method (Attribute definition) takes O(N) operations. We first estimate the albedo of each point of the two range images

Experiments

We evaluated our method using synthetic and real data and compared it with ICPA and ICP using both chromaticity and geometric features (which we call ICP-CG). This comparative study is thus useful for determining the effectiveness of different methods of registering overlapping range images of Lambertian surfaces devoid of salient geometric features. We selected these two methods for two main reasons:

  • ICPA is, to the best of our knowledge, the most recent method that uses the albedo for

Conclusion

We introduced region-based registration of range images using reflectance attributes obtained under rough estimates of illumination conditions. Our method stably extracts reliable attributes that capture the local distribution of albedo on the object surface. These attributes are defined by adaptively growing regions that are generated using a level-set method. Such attributes are used to evaluate the similarity of points to robustly obtain correspondences in points even under rough estimates

Acknowledgment

This work was in part supported by JST, CREST.

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