The monogenic signal consists of an image and its first-order Riesz transform. It describes signal structure as a sinusoid with a particular amplitude, phase and orientation; however, the orientation estimate is poor around certain phase values. We describe a novel method of estimating this sinusoidal signal model using higher-order Riesz transforms, such that amplitude, phase and orientation estimates are improved under noise conditions. Furthermore, the method leads to novel intrinsically-1D (line and edge) and intrinsically-2D (corner and junction) detectors.

We introduce a new second-order method of texture analysis called Adaptive Multi-Scale Grey Level Co-occurrence Matrix (AMSGLCM), based on the well-known Grey Level Co-occurrence Matrix (GLCM) method. The method deviates significantly from GLCM in that features are extracted, not via a fixed 2D weighting function of co-occurrence matrix elements, but by a variable summation of matrix elements in 3D localized neighborhoods. We subsequently present a new methodology for extracting optimized, highly discriminant features from these localized areas using adaptive Gaussian weighting functions. Genetic Algorithm (GA) optimization is used to produce a set of features whose classification "worth" is evaluated by discriminatory power and feature correlation considerations. We critically appraised the performance of our method and GLCM in pairwise classification of images from visually similar texture classes, captured from Markov Random Field (MRF) synthesized, natural, and biological origins. In these cross-validated classification trials, our method demonstrated significant benefits over GLCM, including increased feature discriminatory power, automatic feature adaptability, and significantly improved classification performance.

Chen and Yan presented (ibid., vol.11, p.694-700, 1989) a theorem concerning zero crossings of boundary curvature under morphological openings. In this correspondence, we show by means of a counterexample a flaw in this theorem and suggest how the theorem may be modified to make it correct.

Statistical geometric features (SGF) have recently been proposed for the classification of image textures. The SGF method is easily extended to use other geometric properties of connected regions. Following a brief review of the method, we propose such an extension to the set of SCF features for the purpose of classifying cervical cell textures. The resulting method proves to be as powerful as the gray level co-occurrence matrix (GLCM) method of texture analysis, when tested on a set of 117 cervical cell images. The ability to define features tailored to the geometric properties of the textures concerned makes this method a powerful analysis tool.

A multiscale morphological dilation-erosion smoothing operation and its associated scale-space expansion for multidimensional signals are proposed. Properties of this smoothing operation are developed and, in particular a scale-space monotonic property for signal extrema is demonstrated. Scale-space fingerprints from this approach have advantages over Gaussian scale-space fingerprints in that: they are defined for negative values of the scale parameter; have monotonic properties in two and higher dimensions; do not cause features to be shifted by the smoothing; and allow efficient computation. The application of reduced multiscale dilation-erosion fingerprints to the surface matching of terrain is demonstrated.

After introducing several results relating to the modification of the homotopy of gradient functions based on extrema in the base image and building on earlier results in morphological scale-space, we introduce a scale-space monotonicity theorem for regions of an image defined by watersheds of a gradient function modified to retain only the local minima or maxima of its smoothed parent image. We then illustrate the theorem with an example of the scale-space extraction of texture features from the nuclei of cervical cells.

We present the theory of multiscale dilation-erosion scale-space and the process of feature extraction via morphological scale-space fingerprints. We then discuss the reduced form of the fingerprints and state the scale-space causality theorem. These fingerprints are then applied to the recognition of multiple objects from range data. The proposed recognition system is invariant to translation, rotation, scale, and partial occlusion. We demonstrate results for the recognition of human faces in a scene, and the recognition of mountain features in a digital elevation map.>

Scale-space is an important recent concept used in image processing and pattern recognition. Traditional scale-space is generated by a linear smoothing operation. The author presents a nonlinear type of smoother related to mathematical morphology which meets (modified) 'scale-space axioms' and also generates a 'scale-space'. This scale-space is full-plane and preserves the positions of features.>