The authors describe a general-purpose, representation-independent method for the accurate and computationally efficient registration of 3-D shapes including free-form curves and surfaces. The method handles the full six degrees of freedom and is based on the iterative closest point (ICP) algorithm, which requires only a procedure to find the closest point on a geometric entity to a given point. The ICP algorithm always converges monotonically to the nearest local minimum of a mean-square distance metric, and the rate of convergence is rapid during the first few iterations. Therefore, given an adequate set of initial rotations and translations for a particular class of objects with a certain level of 'shape complexity', one can globally minimize the mean-square distance metric over all six degrees of freedom by testing each initial registration. One important application of this method is to register sensed data from unfixtured rigid objects with an ideal geometric model, prior to shape inspection. Experimental results show the capabilities of the registration algorithm on point sets, curves, and surfaces. >

A method for registration of 3-D shapes

Clustering is the unsupervised classification of patterns (observations, data items, or feature vectors) into groups (clusters). The clustering problem has been addressed in many contexts and by researchers in many disciplines; this reflects its broad appeal and usefulness as one of the steps in exploratory data analysis. However, clustering is a difficult problem combinatorially, and differences in assumptions and contexts in different communities has made the transfer of useful generic concepts and methodologies slow to occur. This paper presents an overview of pattern clustering methods from a statistical pattern recognition perspective, with a goal of providing useful advice and references to fundamental concepts accessible to the broad community of clustering practitioners. We present a taxonomy of clustering techniques, and identify cross-cutting themes and recent advances. We also describe some important applications of clustering algorithms such as image segmentation, object recognition, and information retrieval.

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Data clustering: a review

Machine Learning is the study of methods for programming computers to learn. Computers are applied to a wide range of tasks, and for most of these it is relatively easy for programmers to design and implement the necessary software. However, there are many tasks for which this is difficult or impossible. These can be divided into four general categories. First, there are problems for which there exist no human experts. For example, in modern automated manufacturing facilities, there is a need to predict machine failures before they occur by analyzing sensor readings. Because the machines are new, there are no human experts who can be interviewed by a programmer to provide the knowledge necessary to build a computer system. A machine learning system can study recorded data and subsequent machine failures and learn prediction rules. Second, there are problems where human experts exist, but where they are unable to explain their expertise. This is the case in many perceptual tasks, such as speech recognition, hand-writing recognition, and natural language understanding. Virtually all humans exhibit expert-level abilities on these tasks, but none of them can describe the detailed steps that they follow as they perform them. Fortunately, humans can provide machines with examples of the inputs and correct outputs for these tasks, so machine learning algorithms can learn to map the inputs to the outputs. Third, there are problems where phenomena are changing rapidly. In finance, for example, people would like to predict the future behavior of the stock market, of consumer purchases, or of exchange rates. These behaviors change frequently, so that even if a programmer could construct a good predictive computer program, it would need to be rewritten frequently. A learning program can relieve the programmer of this burden by constantly modifying and tuning a set of learned prediction rules. Fourth, there are applications that need to be customized for each computer user separately. Consider, for example, a program to filter unwanted electronic mail messages. Different users will need different filters. It is unreasonable to expect each user to program his or her own rules, and it is infeasible to provide every user with a software engineer to keep the rules up-to-date. A machine learning system can learn which mail messages the user rejects and maintain the filtering rules automatically. Machine learning addresses many of the same research questions as the fields of statistics, data mining, and psychology, but with differences of emphasis. Statistics focuses on understanding the phenomena that have generated the data, often with the goal of testing different hypotheses about those phenomena. Data mining seeks to find patterns in the data that are understandable by people. Psychological studies of human learning aspire to understand the mechanisms underlying the various learning behaviors exhibited by people (concept learning, skill acquisition, strategy change, etc.).

Machine learning

We describe a technique for image encoding in which local operators of many scales but identical shape serve as the basis functions. The representation differs from established techniques in that the code elements are localized in spatial frequency as well as in space. Pixel-to-pixel correlations are first removed by subtracting a lowpass filtered copy of the image from the image itself. The result is a net data compression since the difference, or error, image has low variance and entropy, and the low-pass filtered image may represented at reduced sample density. Further data compression is achieved by quantizing the difference image. These steps are then repeated to compress the low-pass image. Iteration of the process at appropriately expanded scales generates a pyramid data structure. The encoding process is equivalent to sampling the image with Laplacian operators of many scales. Thus, the code tends to enhance salient image features. A further advantage of the present code is that it is well suited for many image analysis tasks as well as for image compression. Fast algorithms are described for coding and decoding.

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The Laplacian Pyramid as a Compact Image Code

A theory of edge detection is presented. The analysis proceeds in two parts. (1) Intensity changes, which occur in a natural image over a wide range of scales, are detected separately at different scales. An appropriate filter for this purpose at a given scale is found to be the second derivative of a Gaussian, and it is shown that, provided some simple conditions are satisfied, these primary filters need not be orientation-dependent. Thus, intensity changes at a given scale are best detected by finding the zero values of delta 2G(x,y)*I(x,y) for image I, where G(x,y) is a two-dimensional Gaussian distribution and delta 2 is the Laplacian. The intensity changes thus discovered in each of the channels are then represented by oriented primitives called zero-crossing segments, and evidence is given that this representation is complete. (2) Intensity changes in images arise from surface discontinuities or from reflectance or illumination boundaries, and these all have the property that they are spatially. Because of this, the zero-crossing segments from the different channels are not independent, and rules are deduced for combining them into a description of the image. This description is called the raw primal sketch. The theory explains several basic psychophysical findings, and the operation of forming oriented zero-crossing segments from the output of centre-surround delta 2G filters acting on the image forms the basis for a physiological model of simple cells (see Marr & Ullman 1979).

http://www.hms.harvard.edu/bss/neuro/bornlab/qmbc/beta/day4/marr-hildreth-edge-prsl1980.pdf

Theory of Edge Detection

An approach is presented for planning sensing strategies dynamically on the basis of the system's current best information about the world. The approach is for the system to propose a sensing operation automatically and then to determine the maximum ambiguity which might remain in the world description if that sensing operation were applied. The system then applies that sensing operation which minimizes this ambiguity. To do this, the system formulates object hypotheses and assesses its relative belief in those hypotheses to predict what features might be observed by a proposed sensing operation. Furthermore, since the number of sensing operations available to the system can be arbitrarily large, equivalent sensing operations are grouped together using a data structure that is based on the aspect graph. In order to measure the ambiguity in a set of hypotheses, the authors apply the concept of entropy from information theory. This allows them to determine the ambiguity in a hypothesis set in terms of the number of hypotheses and the system's distribution of belief among those hypotheses. >

Planning sensing strategies in a robot work cell with multi-sensor capabilities

Local data aggregation is an effective means to save sensor node energy and prolong the lifespan of wireless sensor networks. However, when a sensor network is used to track moving objects, the task of local data aggregation in the network presents a new set of challenges, such as the necessity to estimate, usually in real time, the constantly changing state of the target based on information acquired by the nodes at different time instants. To address these issues, we propose a distributed object tracking system which employs a cluster-based Kalman filter in a network of wireless cameras. When a target is detected, cameras that can observe the same target interact with one another to form a cluster and elect a cluster head. Local measurements of the target acquired by members of the cluster are sent to the cluster head, which then estimates the target position via Kalman filtering and periodically transmits this information to a base station. The underlying clustering protocol allows the current state and uncertainty of the target position to be easily handed off among clusters as the object is being tracked. This allows Kalman filter-based object tracking to be carried out in a distributed manner. An extended Kalman filter is necessary since measurements acquired by the cameras are related to the actual position of the target by nonlinear transformations. In addition, in order to take into consideration the time uncertainty in the measurements acquired by the different cameras, it is necessary to introduce nonlinearity in the system dynamics. Our object tracking protocol requires the transmission of significantly fewer messages than a centralized tracker that naively transmits all of the local measurements to the base station. It is also more accurate than a decentralized tracker that employs linear interpolation for local data aggregation. Besides, the protocol is able to perform real-time estimation because our implementation takes into consideration the sparsity of the matrices involved in the problem. The experimental results show that our distributed object tracking protocol is able to achieve tracking accuracy comparable to the centralized tracking method, while requiring a significantly smaller number of message transmissions in the network.

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Distributed Object Tracking Using a Cluster-Based Kalman Filter in Wireless Camera Networks

In this report we have used projectivity theory to model the process of structured light scanning for 3D robot vision. The projectivity formalism is used to derive a 4 × 3 transformation matrix that converts points in the image plane into their corresponding 3D world coordinates. Calibration of the scanner consists of computing the coefficient of this matrix by showing to the system a set of lines generated by suitable object edges. We end this paper by showing how the matrix can be used to convert image pixel locations into the world coordinates of the corresponding object points using two different scanning strategies.

Modeling and calibration of a structured light scanner for 3-D robot vision

Ultrasonic B-scan imaging: theory of image formation and a technique for restoration.

The authors show how large efficiencies can be achieved in model-based 3-D vision by combining the notions of discrete relaxation and bipartite matching. The computational approach presented is capable of pruning large segments of search space-an indispensable step when the number of objects in the model library is large and when recognition of complex objects with a large number of surfaces is called for. Bipartite matching is used for quick wholesale rejection of inapplicable models and for the determination of compatibility of a scene surface with a potential model surface taking into account relational considerations. The time complexity function associated with those aspects of the procedure that are implemented via bipartite matching is provided. The algorithms do not take more than a couple of iterations, even for objects with more than 30 surfaces. >

Avinash C. Kak

Papers

Planning sensing strategies in a robot work cell with multi-sensor capabilities

Distributed Object Tracking Using a Cluster-Based Kalman Filter in Wireless Camera Networks

Modeling and calibration of a structured light scanner for 3-D robot vision

Ultrasonic B-scan imaging: theory of image formation and a technique for restoration.

3-D object recognition using bipartite matching embedded in discrete relaxation