The authors comments that Charif-Chefchaouni and Schonfeld (see ibid., vol.3, no.6, p.847, 1994) investigated the invertibility of a morphological representation of binary images and determined the necessary and sufficient conditions for its inverse. The authors show that one of the derived necessary conditions is not valid. A counterexample is given to illustrate our observations. Charif-Chefchaouni and Schonfeld reply that the new sufficient condition is proposed for the invertibility of the morphological image representation. A modification of its inverse is subsequently used to derive a new necessary condition for the invertibility of the morphological image representation. A composition of these conditions is finally used to provide a new necessary and sufficient condition under some restrictions for the invertibility of the morphological image representation. These necessary and sufficient conditions form a revision of one of the necessary conditions for the invertibility of the morphological image representation stated in the original paper.

Proposes an image enhancement algorithm that converts raw data from a storage phosphor scanner into a diagnostically optimized image. The spatial segmentation algorithm is applied to extract the body part of a clinical image, and histogram analysis is then used to develop the tone-scale for the region of interest. Further enhancement is obtained by unsharp masking. This approach reduces the sensitivity to nonanatomical regions and allows full use of the display's dynamic range for image viewing. The algorithms have been tested on clinical images and the results were reviewed by radiologists. Currently, these algorithms are being successfully used in the clinical environment.>

We describe a multiple-scale boundary representation based on morphological operations. An object boundary is first progressively smoothed by a number of opening and closing operations using a set of structuring elements of increasing size, generating a multiple scale representation of the object. Then, corresponding features of the smoothed boundary across a continuum of scales are extracted and linked together forming a map called the morphological scale space. Properties of this scale space map are investigated and presented. A shape smoothing algorithm, which is based on this map and its properties, is proposed to show how the scale space representation could be applied to solve practical image processing problems. Specifically, in line with Witkin's (1983) Gaussian scale space filtering, boundary features that are explicitly related across scales by the morphological scale space map are organized into global region information and local boundary features. From the organization, perceptually dominant features are determined and a shape is smoothed without the requirement of prior knowledge of the object boundary nor its noise.>

This paper describes a reconstructable thinning process which is based on one-pass parallel thinning and the morphological skeleton transformation. It reduces a binary digital pattern into a unit-width connected skeleton enabling perfect reconstruction of the original pattern. The process uses thinning templates to iteratively remove boundary pixels and structuring templates of the morphological skeleton transformation to retain critical feature pixels for reconstruction. The thinning templates together with the extracted feature pixels ensure skeletal connectivity, unit width, and reconstructability. These essential properties are guaranteed regardless of the chosen structuring templates used in the morphological skeleton transformation. The thinning process is analyzed and results are presented. A number of implementation issues, such as the choice of structuring templates, the computational model, noise filtering, and computational efficiency, are also addressed.

A one-pass parallel thinning algorithm based on a number of criteria, including connectivity, unit-width convergence, medial axis approximation, noise immunity, and efficiency, is proposed. A pipeline processing model is assumed for the development. Precise analysis of the thinning process is presented to show its properties, and proofs of skeletal connectivity and convergence are provided. The proposed algorithm is further extended to the derived-grid to attain an isotropic medial axis representation. A set of measures based on the desired properties of thinning is used for quantitative evaluation of various algorithms. Image reconstruction from connected skeletons is also discussed. Evaluation shows that the procedures compare favorably to others.>

A precise definition of digital skeletons and a mathematical framework for the analysis of a class of thinning algorithms, based on morphological set transformation, are presented. A particular thinning algorithm (algorithm A) is used as an example in the analysis. Precise definitions and analyses associated with the thinning process are presented, including the proof of convergence, the condition for one-pixel-thick skeletons, and the connectedness of skeletons. In addition, a necessary and sufficient condition for the thinning process in general is derived, and an algorithm (algorithm B) based on this condition is developed. Experimental results are used to compare the two thinning algorithms, and issues involving noise immunity and skeletal bias are addressed.>