# Morphological retail analysis

Morphological retail analysis is a way to precisely outline a trading area. Managing trade areas is an old marketing problem and a major concern for retail and service firms, especially with the development of retail and service networks. It seems to be to day a critical point in the development of geomarketing techniques. But how to manage such an area without any precise definition and delineation ?

According to Ghosh and McLafferty (1987), the trade area is "the geographic area from which the store draws most of its customers and within market penetration is highest". Huff (1964) describes it as a statistical and more extended concept, "a geographically delineated region containing potential customers for whom there exists a probability greater than zero of their purchasing a given class of products or services offered for sale by a particular firm or by a particular agglomeration of firms".

Even though that constitutes a challenge, defining or keeping an eye on trade areas boundaries and specification is strategic for the survival of existing outlets or for projecting the creation of new retail or service firms. In the first case, a trade area analysis serves mainly to continuously adapt the marketing policy to attract as much customers as possible and to maintain and develop its goodwill counterbalancing competitor drawing. In the second case, evaluating trade areas gives the opportunity to judge a business investment at a specific geographic location as well as making sales estimates and determining a future marketing strategy.

Mathematical morphology based on concepts of topology, signal processing, probabilities and graph theory comprises a great number of applications which all concern the real world. The fields interested by this technique are various and can be for example materials science, geology, biology, geography, robotics. The method based on mathematical morphology to outline a trading area can be described in a sequence of stages:

• Data coding and mapping - Each address of a customer Ci belonging to a database corresponds to a lit point is represented by a black pixel of co-ordinates (xi, yi) in a perpendicular base (OX,OY): A mapping of the customers is obtained.
• Pretreatment of the data - The pretreatment of the data of investigation is intended to facilitate the analysis of the data without reducing the quality of available information. Stemming from signal processing, the principal method consists of an undulatory filtering (an image or an investigation into a geographical sector being a two-dimensional wave).
• Segmentation of the data - The binary dilatation is a morphological process which causes to increase the total surface of this set. It tends to connect the disjoined parts and to smooth contours in a picture. Another morphological transformation is the binary erosion which smooths also surface but on the contrary tends to decrease the total surface of the set. The morphological transformation of closing combines dilatation and erosion.

The morphological transformation of the " top hat " is the subtraction of the data of the initial mapping with the data of the closed matrix. It constitutes the morphological filter that thus underlines contours of the trading area.

## References

Jerome Baray, Gerard Cliquet, 2007, European Journal of Operational Research, N°182
Serra, J., 1982. Image Analysis and Mathematical Morphology, Academic Press,