Gradient watersheds in morphological scale-space

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.     

Improved morphological top-hat

An improved morphological top-hat transform is presented which offers improved detection of light or dark image blobs in the presence of certain types of noise     

Scale-space properties of the multiscale morphologicaldilation-erosion

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     

Gradient based intensity normalization

Intensity normalization is important in quantitative image analysis, especially when extracting features based on intensity. In automated microscopy, particularly in large cellular screening experiments, each image contains objects of similar type (e.g. cells) but the object density (number and size of the objects) may vary markedly from image to image. Standard intensity normalization methods, such as matching the grey-value histogram of an image to a target histogram from, i.e. a reference image, only work well if both object type and object density are similar in the images to be matched. This is typically not the case in cellular screening and many other types of images where object type varies little from image to image, but object density may vary dramatically. In this paper, we propose an improved form of intensity normalization which uses grey-value as well as gradient information. This method is very robust to differences in object density. We compare and contrast our method with standard histogram normalization across a range of image types, and show that the modified procedure performs much better when object density varies between images.     

On the scale-space theorem of Chen and Yan

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     

On Computing the Exact Euclidean Distance Transform on Rectangular and Hexagonal Grids

In this paper we prove an equivalence relation between the distance transform of a binary image, where the underlying distance is based on a positive definite quadratic form, and the erosion of its characteristic function by an elliptic poweroid structuring element. The algorithms devised by Shih and Mitchell [18] and Huang and Mitchell [7], for calculating the exact Euclidean distance transform (EDT) of a binary digital image manifested on a square grid, are particular cases of this result. The former algorithm uses erosion by a circular cone to calculate the EDT whilst the latter uses erosion by an elliptic paraboloid (which allows for pixel aspect ratio correction) to calculate the square of the EDT. Huang and Mitchell's algorithm [7] is arguably the better of the two because: (i) the structuring element can be decomposed into a sequence of dilations by 3 × 3 structuring elements (a similar decomposition is not possible for the circular cone) thus reducing the complexity of the erosion, and (ii) the algorithm only requires integer arithmetic (it produces squared distance). The algorithm is amenable to both hardware implementation using a pipeline architecture and efficient implementation on serial machines. Unfortunately the algorithm does not directly transpose to, nor has a corresponding analogue on, the hexagonal grid (the same is also true for Shih and Mitchell's algorithm [7]). In this paper, however, we show that if the hexagonal grid image is embedded in a rectangular grid then Huang and Mitchell's algorithm [7] can be applied, with aspect ratio correction, to obtain the exact EDT on the hexagonal grid.