A formal de nition of morphological operators in (max,min)algebra is introduced and their relevant properties from an algebraic viewpoint are stated. Some previous works in mathematical morphology have already encountered this type of operators but a systematic study of them has not yet been undertaken in the morphological literature. It is shown in particular that one of their fundamental prop...

Since image analysis techniques have come to maturity, mesh analysis has remained challenging requiring more and more efforts for elaborating an effective theoretical model. In this article, following algebraic mesh operators, we introduce algorithms that perform morphological transformations on unorganized point sets connected by their Delaunay triangulations. We show that these algorithms cor...

The median operator is a nonlinear (morphological) image transformation which has become very popular because it can suppress noise while preserving the edges. I t treats the foreground and background of an image in an identical way, that is, it is a self-dual operator. Unfortunately, the median operator lacks the idempotence property: it is not a morphological filter. This paper gives a comple...

Since image analysis techniques have come to maturity, mesh analysis has remained challenging requiring more and more efforts for elaborating an effective theoretical model. In this article, following algebraic mesh operators, we introduce algorithms that perform morphological transformations on unorganized point sets connected by their Delaunay triangulations. We show that these algorithms cor...

The LULU operators for sequences are extended to multi-dimensional arrays via the morphological concept of connection in a way which preserves their essential properties, e.g. they are separators and form a four element fully ordered semi-group. The power of the operators is demonstrated by deriving a total variation preserving discrete pulse decomposition of images.

This paper proposes a general algebraic construction technique for image scale-spaces. The basic idea is to rst downscale the image by some factor using an invertible scaling, then apply an image operator (linear or morphological) at a unit scale, and nally resize the image to its original scale. It is then required that the resulting one-parameter family of image operators satisses the semigro...

Many useful morphological filters are built as long concatenations of erosions and dilations: openings, closings, size distributions, sequential filters, etc. This paper proposes a new algorithm implementing morphological dilation and erosion of functions. It supports rectangular structuring element, runs in linear time w.r.t. the image size and constant time w.r.t. the structuring element size...

This paper discusses the construction of perfect reconstruction filter banks using morphological operators. Two concrete examples are given: (i) the morphological Haar wavelet, and (ii) a wavelet decomposition obtained from the lifting scheme which has the nice property that local maxima are being preserved.

We describe investigations applying grey-scale mathematical morphology to the problem of feature detection. We show how a combination of morphological operators can be interpreted in terms of the differential geometrical characteristics of the intensity surface. This is significant in that it provides insight into how morphological operators manipulate image data in a manner that has no paralle...

This paper proposes a general algebraic construction technique for image scale-spaces. The basic idea is to rst downscale the image by some factor using an invertible scaling, then apply an image operator (linear or morphological) at a unit scale, and nally resize the image to its original scale. It is then required that the resulting one-parameter family of image operators satis es the semigro...