Scale Space Image Research Articles

A matching algorithm of deformed planar curves using multiscale convex/concave structures

AbstractThis paper proposes a new multiscale segment matching method which is applicable to heavily deformed planar shapes. First, multiscale representations are obtained using curvature scale space filtering. Then inflection point correspondence is developed between consecutive smoothed shapes. The representation in this paper, unlike the well‐known curvature scale space image description, ensures that it always satisfies the consistency of hierarchical segment replacement. Moreover, it requires less processing time and memory allocation. Finally, optimum scale segments are matched by a new multiscale segment matching method proposed herein. In this method, the matching problem is formulated as a minimization problem of the total amount of segment dissimilarity. The minimization problem is solved effectively using dynamic programming. The proposed matching method makes it possible to obtain intuitively relevant correspondences even if the shapes have some local heavy deformation.

Symbolic construction of a 2-D scale-space image

A symbolic approach to constructing a multiscale primitive shape description to 2-D binary (silhouette) shape images is presented. In contrast to contour or region smoothing techniques, grouping operations are performed over collections of tokens residing on a scale-space blackboard. Two types of grouping operations are identified that, respectively, aggregate edge primitives at one scale into edge primitives at a coarser scale and group edge primitives into partial-region assertions, including curved contours, primitive corners, and bars. Procedures to perform these computations are presented. >

A multiscanning approach based on morphological filtering

It is argued that the mathematical morphology method seems to be more reasonable and powerful in studying certain multiscaling vision problems than the approach that uses derivatives of Gaussian-shaped filters of different sizes. To show the validity of this method, the authors concentrated on an application that involves forming scale-space image of a 2-D shape using morphological opening filtering. A proof is given to show that morphological opening filtering has a property of not introducing additional zero-crossings as one moves to a coarser scale. This is a different result from the conclusion by A.L. Yuille and T.A. Poggio (ibid., vol.PAMI-8, Jan. 1986) that the Gaussian filter is the only filter with this property. In addition, opening filtering is computationaly simpler than the Gaussian filter.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Comments on fingerprints of two-dimensional edge models

Shah, Sood, and Jain (Comput. Vision Graphics Image Process34, 1986, 321–343) have recently published an interesting scale-space analysis of pulse and staircase edge models, both one- and two-dimensional. In this note we comment upon Shah, Sood, and Jain's analysis of the two-dimensional step edge, pulse edge, and staircase edge models. Their derivation of the scale-space images and fingerprints can be simplified by taking advantage of a key geometric feature of Gaussian filters, namely, rotational invariance. The fingerprints of these three models can easily and directly be geometrically deduced from the fingerprints of the one-dimensional models. The fingerprints should be viewed as cylinders over a base curve which is precisely the fingerprint of the corresponding one-dimensional edge model. In this way fingerprints of the two-dimensional models can be immediately visualized from their one-dimensional counterparts. We also demonstrate that the range of influence of one edge upon another edge located a distance daway begins at a scale of d/3.

Scale based algorithm for recognition of blurred planar objects

The paper presents an algorithm based on scale-space analysis, for the recognition of blurred planar objects. Apart from satisfying the usual requirements for invariance under translation, rotation and scaling, the algorithm is also invariant under blurring, that is, across all levels of detail or scales. The technique makes use of the spatial coincidence of the infiexion points on the object contour at all scales, and of the fact that no new such points are created as the object becomes more blurred. The algorithm therefore searches for the best match of these points at a single scale in the scale-space image. The algorithm was implemented on an IBM/AT in Modula-2 programming language, and was tested out on a group of 20 geographical maps of different sizes and at varying distances from the camera. A recognition rate of 95 to 100% and an average recognition time of 2.5 seconds were obtained by an efficient organisation of the template dictionary.

Symbolic representation of hyperspectral data

We have developed a symbolic representation of hyperspectral data using the scale space techniques of Witkin. We created a scale space image of hyperspectral data from convolution with Gaussian masks and then a fingerprint that extracts individual features from the original data. The fingerprint provides a context that pairs inflection points and assigns them to a feature, generates a measure of importance for each feature, and relates features to each other. The representation is an ordered sequence of triplets containing a measure of importance related to the area of each feature and the left and right inflection points of the feature. The description is compact, quantitative, and hierarchical, describing the hyperspectral curve by its most important structural features first, followed by features of lesser importance.

Efficient technique for scale-space imaging of planar objects

The scale-space image, i.e. the plot of the location of the inflection points against the scale of the Gaussian smoothing filter, is an effective description for planar object recognition. Recent techniques of scale-space imaging involve four convolutions for each scale, while our technique by smoothing the curvature of the object contour directly requires only one convolution per scale.

Scale-Based Description and Recognition of Planar Curves and Two-Dimensional Shapes

The problem of finding a description, at varying levels of detail, for planar curves and matching two such descriptions is posed and solved in this paper. A number of necessary criteria are imposed on any candidate solution method. Path-based Gaussian smoothing techniques are applied to the curve to find zeros of curvature at varying levels of detail. The result is the ``generalized scale space'' image of a planar curve which is invariant under rotation, uniform scaling and translation of the curve. These properties make the scale space image suitable for matching. The matching algorithm is a modification of the uniform cost algorithm and finds the lowest cost match of contours in the scale space images. It is argued that this is preferable to matching in a so-called stable scale of the curve because no such scale may exist for a given curve. This technique is applied to register a Landsat satellite image of the Strait of Georgia, B.C. (manually corrected for skew) to a map containing the shorelines of an overlapping area.