Planning algorithms are impacting technical disciplines and industries around the world, including robotics, computer-aided design, manufacturing, computer graphics, aerospace applications, drug design, and protein folding. This coherent and comprehensive book unifies material from several sources, including robotics, control theory, artificial intelligence, and algorithms. The treatment is centered on robot motion planning but integrates material on planning in discrete spaces. A major part of the book is devoted to planning under uncertainty, including decision theory, Markov decision processes, and information spaces, which are the “configuration spaces” of all sensor-based planning problems. The last part of the book delves into planning under differential constraints that arise when automating the motions of virtually any mechanical system. Developed from courses taught by the author, the book is intended for students, engineers, and researchers in robotics, artificial intelligence, and control theory as well as computer graphics, algorithms, and computational biology.

Planning Algorithms: Introductory Material

The ICP (Iterative Closest Point) algorithm is widely used for geometric alignment of three-dimensional models when an initial estimate of the relative pose is known. Many variants of ICP have been proposed, affecting all phases of the algorithm from the selection and matching of points to the minimization strategy. We enumerate and classify many of these variants, and evaluate their effect on the speed with which the correct alignment is reached. In order to improve convergence for nearly-flat meshes with small features, such as inscribed surfaces, we introduce a new variant based on uniform sampling of the space of normals. We conclude by proposing a combination of ICP variants optimized for high speed. We demonstrate an implementation that is able to align two range images in a few tens of milliseconds, assuming a good initial guess. This capability has potential application to real-time 3D model acquisition and model-based tracking.

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Efficient variants of the ICP algorithm

We describe a hardware and software system for digitizing the shape and color of large fragile objects under non-laboratory conditions Our system employs laser triangulation rangefinders, laser time-of-flight rangefinders, digital still cameras, and a suite of software for acquiring, aligning, merging, and viewing scanned data As a demonstration of this system, we digitized 10 statues by Michelangelo, including the well-known figure of David, two building interiors, and all 1,163 extant fragments of the Forma Urbis Romae, a giant marble map of ancient Rome Our largest single dataset is of the David - 2 billion polygons and 7,000 color images In this paper, we discuss the challenges we faced in building this system, the solutions we employed, and the lessons we learned We focus in particular on the unusual design of our laser triangulation scanner and on the algorithms and software we developed for handling very large scanned models

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The digital Michelangelo project: 3D scanning of large statues

The digitization of the 3D shape of real objects is a rapidly expanding field, with applications in entertainment, design, and archaeology. We propose a new 3D model acquisition system that permits the user to rotate an object by hand and see a continuously-updated model as the object is scanned. This tight feedback loop allows the user to find and fill holes in the model in real time, and determine when the object has been completely covered. Our system is based on a 60 Hz. structured-light rangefinder, a real-time variant of ICP (iterative closest points) for alignment, and point-based merging and rendering algorithms. We demonstrate the ability of our prototype to scan objects faster and with greater ease than conventional model acquisition pipelines.

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Real-time 3D model acquisition

In this paper we describe a novel technique for detecting salient regions in an image. The detector is a generalization to affine invariance of the method introduced by Kadir and Brady [10]. The detector deems a region salient if it exhibits unpredictability in both its attributes and its spatial scale.

An affine invariant salient region detector

A strategy for acquiring 3-D data of an unknown scene, using range images obtained by a light stripe range finder is addressed. The foci of attention are occluded regions, i.e., only the scene at the borders of the occlusions is modeled to compute the next move. Since the system has knowledge of the sensor geometry, it can resolve the appearance of occlusions by analyzing them. The problem of 3-D data acquisition is divided into two subproblems due to two types of occlusions. An occlusion arises either when the reflected laser light does not reach the camera or when the directed laser light does not reach the scene surface. After taking the range image of a scene, the regions of no data due to the first kind of occlusion are extracted. The missing data are acquired by rotating the sensor system in the scanning plane, which is defined by the first scan. After a complete image of the surface illuminated from the first scanning plane has been built, the regions of missing data due to the second kind of occlusions are located. Then, the directions of the next scanning planes for further 3-D data acquisition are computed. >

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Occlusions as a guide for planning the next view

In this work, we present a new approach to interest point detection. Different types of features in images are detected by using a common computational concept. The proposed approach considers the total variability of local regions. The total sum of squares computed on the intensity values of a local circular region is divided into three components: between-circumferences sum of squares, between-radii sum of squares, and the remainder. These three components normalized by the total sum of squares represent three new saliency measures, namely, radial, tangential, and residual. The saliency measures are computed for regions with different radii and scale spaces are built in this way. Local extrema in scale space of each of the saliency measures are located. They represent features with complementary image properties: blob-like features, corner-like features, and highly textured points. Results obtained on image sets of different object classes and image sets under different types of photometric and geometric transformations show high robustness of the method to intraclass variations as well as to different photometric transformations and moderate geometric transformations and compare favorably with the results obtained by the leading interest point detectors from the literature. The proposed approach gives a rich set of highly distinctive local regions that can be used for object recognition and image matching.

Self-Similarity and Points of Interest

The task of constructing a volumetric description of a scene from a single image is an underdetermined problem, whether it is a range or an intensity image. To resolve the ambiguities that are caused by occlusions in images, we need to take sensor measurements from several different views. We have limited ourselves to the range images obtained by a laser scanning system. It is an active binocular system which can encounter two types of occlusions. An occlusion arises either when the reflected laser light does not reach the camera or when the directed laser light does not reach the scene surface. The task of 3-D data acquisition is divided into two subproblems: to see what is illuminated and to properly direct the illuminating plane to illuminate the entire scene. The first kind of occlusions are easily detected and can be used in designing an efficient algorithm. We develop a strategy to determine the sequence of different views using the information in a narrow zone around the occluded regions. Occluded regions are approximated by polygons. Based on the height information of the border of the occluded regions and geometry of the edges of the polygonal approximation, the next views in the same scanning plane are determined. From the acquired information in the first scanning plane the directions of the next scanning planes are computed.

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How to Decide From the First View Where to Look Next

We present in this paper an approach to a typical task of active sensing, namely how to successively position the sensor in order to accomplish a given task. The approach is general in the sense that it does not require a priori information about the constituents of the scene, and data driven in the sense that it is the data that provides the information for driving the planning of the next views. We applied our approach to the task of determining the 3-D coordinates of the points of object silhouettes in the image under orthographic projection.

Planning the Next View Using the Max-Min Principle

Image categorisation involves the well known difficulties with different visual appearances of a single object, but also introduces the problem of within-category variation. This within-category variation makes highly distinctive local descriptors less appropriate for categorisation. Difficulties because of the within category variation and clutter are tackled by modelling image fragments in a new manner. The authors propose a family of local image descriptors, called probabilistic patch descriptors (PPDs). PPDs encode the appearance of image fragments as well as their variability within a category. PPDs extend the usual local descriptors by also modelling the variance of the descriptors' elements, for example pixels or bins in a histogram. To compare two PPDs, and a PPD with an image, a new similarity measure called PPD matching score is introduced. For each object category, a set of representative PPDs is learnt. Images are represented as feature vectors of the best matching scores obtained for representative PPDs in images. Support vector machine classifiers are then trained on the feature vectors. PPDs are applied to image categorisation using machine learning where the features are the matching scores between images and PPDs. The authors experiment with two variants of PPDs that are based on complementary local descriptors. An interesting observation is that combining the two PPD variants improves the accuracy of categorisation. Experiments indicate that the benefits of modelling the within-category variation give results that are comparable with the state-of-the-art categorisation methods, and show good robustness with respect to noise and occlusions.

Jasna Maver

Papers

Occlusions as a guide for planning the next view

Self-Similarity and Points of Interest

How to Decide From the First View Where to Look Next

Planning the Next View Using the Max-Min Principle

Local probabilistic descriptors for image categorisation