Michiel Hagedoorn

State of the art in shape matching

Large image databases are used in an extraordinary number of multimedia applications in fields such as entertainment, business, art, engineering, and science. Retrieving images by their content, as opposed to external features, has become an important operation. A fundamental ingredient for content-based image retrieval is the technique used for comparing images. There are two general methods for image comparison: intensity based (color and texture) and geometry based (shape). A recent user survey about cognition aspects of image retrieval shows that users are more interested in retrieval by shape than by color and texture [62]. However, retrieval by shape is still considered one of the most difficult aspects of content-based search. Indeed, systems such as IBM’s Query By Image Content, QBIC [57], perhaps one of the most advanced image retrieval systems to date, is relatively successful in retrieving by color and texture, but performs poorly when searching on shape. A similar behavior is exhibited in the new Alta Vista photo finder [10].

Reliable and Efficient Pattern Matching Using an Affine Invariant Metric

We present a new pattern similarity measure that behaves well under affine transformations. Our similarity measure is useful for pattern matching since it is defined on patterns with multiple components, satisfies the metric properties, is invariant under affine transformations, and is robust with respect to perturbation and occlusion. We give an algorithm, based on hierarchical subdivision of transformation space, which minimises our measure under the group of affine transformations, given two patterns. In addition, we present results obtained using an implementation of this algorithm.

Shape Similarity Measures, Properties and Constructions

This paper formulates properties of similarity measures. We list a number of similarity measures, some of which are not well known (such as the Monge-Kantorovich metric), or newly introduced (reflection metric), and give a set constructions that have been used in the design of some similarity measures.

A general method for partial point set matching

In applications such as stereo matching, content-baaed image retrieval, object recognition, and radiotherapy alignment, a major problem is finding a transformation which matches part of a point set A to some part of another point set El. For example, A could consist of points extracted from the left image, query image, object model, or patient body data at the planning stage, while the other point set B is formed by points from the right image, database image, range data, or patient body points at the radiation stage. In this short communication, we will present a method for finding transformations which map some subset of A within a specified Hausdorff distante of B, while deciding whether such transformations exists. This method is general in the sense that it works for points of arbitrary dimension, and various clawes of transformations, including scaling, general linear transformation, rotation, translation, scaling and translation, affine transformation, and rigid motion,

Measuring Resemblance of Complex Patterns

On a collection of subsets of a space, fundamentally different metrics may be defined. In pattern matching, it is often required that a metric is invariant for a given transformation group. In addition, a pattern metric should be robust for defects in patterns caused by discretisation and unreliable feature detection. Furthermore, a pattern metric should have sufficient discriminative power. We formalise these properties by presenting five axioms. Finding invariant metrics without requiring such axioms is a trivial problem. Using our axioms, we analyse various pattern metrics, including the Hausdorff distance and the symmetric difference. Finally, we present the reflection metric. This metric is defined on finite unions of n - 1-dimensional hyper-surfaces in IRn. The reflection metric is affine invariant and satisfies our axioms.

Nearest Neighbors Can Be Found Efficiently If the Dimension Is Small Relative to the Input Size

We consider the problem of nearest-neighbor search for a set of n data points in d-dimensional Euclidean space. We propose a simple, practical data structure, which is basically a directed acyclic graph in which each node has at most two outgoing arcs. We analyze the performance of this data structure for the setting in which the n data points are chosen independently from a d-dimensional ball under the uniform distribution. In the average case, for fixed dimension d, we achieve a query time of O(log2 n) using only O(n) storage space. For variable dimension, both the query time and the storage space are multiplied with a dimension-dependent factor that is at most exponential in d. This is an improvement over previously known time-space tradeoffs, which all have a super-exponential factor of at least d� (d) either in the query time or in the storage space. Our data structure can be stored efficiently in secondary memory: In a standard secondary-memory model, for fixed dimension d, we achieve average-case bounds of O((log2 n)/B + log n) query time and O(N) storage space, where B is the block-size parameter and N = n/B. Our data structure is not limited to Euclidean space; its definition generalizes to all possible choices of query objects, data objects, and distance functions.

A New Visibility Partition for Affine Pattern Matching

Visibility partitions play an important role in computer vision and pattern matching. This paper studies a new type of visibility, reflection-visibility, with applications in affine pattern matching: it is used in the definition of the reflection metric between two patterns consisting of line segments. This metric is affine invariant, and robust against noise, deformation, blurring, and cracks. We present algorithms that compute the reflection visibility partition in O((n+k) log(n)+v) randomised time, where k is the number of visibility edges (at most O(n2)), and v is the number of vertices in the partition (at most O(n2+k2)). We use this partition to compute the reflection metric in O(r(nA + nB)) randomised time, for two line segment unions, with nA and nB line segments, separately, where r is the complexity of the overlay of two reflection-visibility partitions (at most O(nA4 + nB4)).