The present paper develops a general methodology for the morphological segmentation of hyperspectral images, i.e., with an important number of channels. This approach, based on watershed, is composed of a spectral classification to obtain the markers and a vectorial gradient which gives the spatial information. Several alternative gradients are adapted to the different hyperspectral functions. Data reduction is performed either by Factor Analysis or by model fitting. Image segmentation is done on different spaces: factor space, parameters space, etc. On all these spaces the spatial/spectral segmentation approach is applied, leading to relevant results on the image

Abstract. This paper extends the use of stochastic watershed, recently introduced by Angulo and Jeulin [1], to unsupervised segmentation of multispectral images. Several probability density functions (pdf), derived from Monte Carlo simulations (M realizations of N random markers), are used as a gradient for segmentation: a weighted marginal pdf a vectorial pdf and a probabilistic gradient. These gradient-like functions are then segmented by a volume-based watershed algorithm to define the R largest regions. The various gradients are computed in multispectral image space and in factor image space, which gives the best segmentation. Results are presented on PLEIADES satellite simulated images.

Abstract. We establish the link between Mathematical Morphology and the map of Asplund's distances between a probe and a grey scale function, using the Logarithmic Image Processing scalar multiplication. We demonstrate that the map is the logarithm of the ratio between a dilation and an erosion of the function by a structuring function: the probe. The dilations and erosions are mappings from the lattice of the images into the lattice of the positive functions. Using a flat structuring element, the expression of the map of Asplund's distances can be simplified with a dilation and an erosion of the image; these mappings stays in the lattice of the images. We illustrate our approach by an example of pattern matching with a non-flat structuring function.

Asplünd's metric, which is useful for pattern matching, consists in a double-sided probing, i.e. the over-graph and the sub-graph of a function are probed jointly. It has previously been defined for grey-scale images using the Logarithmic Image Processing (LIP) framework. LIP is a non-linear model to perform operations between images while being consistent with the human visual system. Our contribution consists in extending the Asplünd's metric to colour and multivariate images using the LIP framework. Asplünd's metric is insensitive to lighting variations and we propose a colour variant which is robust to noise.

A general framework of spatio-spectral segmentation for multispectral images is introduced in this paper. The method is based on classification-driven stochastic watershed by Monte Carlo simulations, and it gives more regular and reliable contours than standard watershed. The present approach is decomposed into several sequential steps. First, a dimensionality reduction stage is performed using Factor Correspondence Analysis method. In this context, a new way to select the factor axes (eigenvectors) according to their spatial information is introduced. Then a spectral classification produces a spectral pre-segmentation of the image. Subsequently, a probability density function (pdf) of contours containing spatial and spectral information is estimated by simulation using a stochastic watershed approach driven by the spectral classification. The pdf of contours is finally segmented by a watershed controlled by markers coming from a regularization of the initial classification.