Regions growing with the stochastic pyramid: Application in landscape ecology

-The stochastic pyramid is introduced in landscape ecology in order to propose a spatial organization model of ecological units in river floodplains. It consists in articulating this parallel generator of random patterns with ecological processes. The stochastic pyramid, based on a hierarchy of seed structures, is used to make regions grow in order to obtain random patterns relating to an a priori model. The first level, represented by the lattice, is obtained after a biased random draw and the upper levels are built with a double controlled process of decimation and expansion of the seeds. The resulting pictures present both deterministic and stochastic spatial patterns according to ecological reality. Image pyramids Random patterns River floodplains Ecological succession I. I N T R O D U C T I O N The stochastic pyramid was first presented as a generator of random patterns on a square lattice. (1) The pertinence of such a generator should be stressed because it can easily generate non-homogeneous, non-convex, anisotropic and multicoloured random patterns, although the classical models, Markov process-based or random pattern-based, generally do not control easily the problems of stationarity and of concavity relating to real patterns. The stochastic pyramid rapidly became a tool used for image segmentation. (2'3~ The underlying idea consists of making regions grow until the best segmentation is reached. (4> The idea is based on the consensus paradigm. (5) Within the present paper we propose a third purpose of the stochastic pyramid: we shall make regions grow in order to obtain random patterns relating to an a priori model. More precisely, this paper presents a spatial organization model of ecological units in river floodplains, based on random patterns and ecological processes36'7) This is initially a problem of landscape ecology since the ecological units are combined in forming landscapes. (8~ We therefore consider the landscape as a particular image because the models in image processing and computer vision are often based on random fields andbecause of their ability to represent an image by a random process controlled only by a few parameters. We shall show that ecological processes can be formalized with schematic rules which integrate the four dimensions of the river hydrosystem. c9> We shall then create a logical tessellation of each functional set of the floodplain, and then we shall be able to attribute to each of these elementary regions 61 the probability of observing each ecological unit. After random draw, we shall obtain a textured image, in which each pixel will be a region. We shall see that the stochastic pyramid can be used to make the pixels grow, in order to create original patterns that wilt correspond to ecological maps. 2. AN ECOLOGICAL PROBLEM