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

Monographs on statistics and applied probability

A review on image segmentation techniques

The authors present a fuzzy validity criterion based on a validity function which identifies compact and separate fuzzy c-partitions without assumptions as to the number of substructures inherent in the data. This function depends on the data set, geometric distance measure, distance between cluster centroids and more importantly on the fuzzy partition generated by any fuzzy algorithm used. The function is mathematically justified via its relationship to a well-defined hard clustering validity function, the separation index for which the condition of uniqueness has already been established. The performance of this validity function compares favorably to that of several others. The application of this validity function to color image segmentation in a computer color vision system for recognition of IC wafer defects which are otherwise impossible to detect using gray-scale image processing is discussed. >

A validity measure for fuzzy clustering

The recognition of objects in three-dimensional space is a desirable capability of a computer vision system. Range images, which directly measure 3-D surface coordinates of a scene, are well suited for this task. In this paper we report a procedure to detect connected planar, convex, and concave surfaces of 3-D objects. This is accomplished in three stages. The first stage segments the range image into ``surface patches'' by a square error criterion clustering algorithm using surface points and associated surface normals. The second stage classifies these patches as planar, convex, or concave based on a non-parametric statistical test for trend, curvature values, and eigenvalue analysis. In the final stage, boundaries between adjacent surface patches are classified as crease or noncrease edges, and this information is used to merge compatible patches to produce reasonable faces of the object(s). This procedure has been successfully applied to a large number of real and synthetic images, four of which we present in this paper.

Segmentation and Classification of Range Images

An evidence-based recognition technique is defined that identifies 3-D objects by looking for their notable features. This technique makes use of an evidence rule base, which is a set of salient or evidence conditions with corresponding evidence weights for various objects in the database. A measure of similarity between the set of observed features and the set of evidence conditions for a given object in the database is used to determine the identity of an object in the scene or reject the object(s) in the scene as unknown. This procedure has polynomial time complexity and correctly identifies a variety of objects in both synthetic and real range images. A technique for automatically deriving the evidence rule base from training views of objects is shown to generate evidence conditions that successfully identify new views of those objects. >

Evidence-based recognition of 3-D objects

Thepurpose ofthepresent investigation istodetermine whether thedeveloping tooth hasaformative influence uponthetissues whichsurround itand,ifso,howfarthe influence extends andhowlongitlasts. Invitro microdissection studies haveindicated thattheenamel organofthedeveloping tooth exerts avariety ofinfluences inwardly uponthemesenchyme within itthedental papilla. Itsepithelium isbelieved toinfluencetheinitial condensation ofmesenchyme toformthedental papilla, thedifferentiationofodontoblasts, andthegeneral shaping ofthetooth crownandroots. However, thepossibility thattheenamel organmightalsoexert influence outwardly uponthe surrounding mesenchyme ofthedental sachasnotbeenexperimentally tested. The transformation ofthedental sacintothedefinitive periodontium, consisting ofthe periodontal ligament andalveolar bone, proceeds simultaneously withthegrowth and development oftheroots. Thissuggests somekindofco-ordinating influence between periodontium development andthedevelopment ofthetooth proper. Inorder totest whether suchaninfluence exists, theenamel organ anddental papilla ofthedeveloping hamster molar weredissected fromtheir dental sacbefore rootformation, transplanted intoconnective tissue whichordinarily doesnotformperiodontium, andallowed to develop. Itwasfoundthatallhealthy specimens recovered after 4weeksinthehost hadorganized periodontium around themselves; this suggests theexistence ofanorganizing influence emanating fromthedeveloping root. Theextent oftheinfluence wasfoundtobelimited totheperiodontal ligament anda relatively thinshell of alveolar bonearound theroots andboneinthespace between theroots. Cells forming bonearound transplants seemtohavebeensupplied bythehost. The stimulus forconversion ofhostcells intoosteoblasts probably camefromtheenamel organanditsderivative-Hertwig's epithelial rootsheath. Thisstimulus wasfound to

Richard Hoffman

Papers

Segmentation and Classification of Range Images

Evidence-based recognition of 3-D objects

Formation of periodontal tissues around subcutaneously transplanted hamster molars.

A test of randomness based on the minimal spanning tree

Mitotic patterns in the developing roots of hamster molars.