TABLE OF CONTENTS In his book Vision [198, p. 51], David Marr wrote that "although the basic elements in our image are the intensity changes, the physical world imposes on these raw intensity changes a wide variety of spatial organizations, roughly independently at different scales," and later [p. 54] we read that "intensity changes occur at different scales in an image, and so their optimal detection requires the use of operators of different sizes." Adelson, Hingorani, and Simoncelli used the same language in [3]: "Images contain information at all scales."
Cartography illustrates this concept very well. Maps contain different informa-tion at different scales. For example, it is impossible to plan a trip to visit the Roman churches in the Poitou-Charentes region using the map of France found on a globe of the earth. Indeed, the villages where these churches are found do not appear on the global representation, whose scale is of the order 1 to 10 7. One can only find these villages on maps whose scale is 1 to 200, 000 or smaller.
Cartographers have developed conventions for dealing with geographic informa-tion by partitioning it into categories that correspond to the different scales, for example, the scales typically used for a city, a department, a region, a country, a continent, and the whole globe, which may range from 1 to 15, 000 to 1 to 10 7. These categories are not entirely independent, and the more important features existing at a given scale are repeated at...
