Traditionally, remote sensing has been the terrain of scientists and national security communities, by whom the urban issues are managed. This study evaluates the application of multispectral images with a Very High Spatial Resolution (VHSR) of 0.6 m/p, in monitoring the formation and transformation of roofs to improve how building types can be changed over time. The test was carried out using two multispectral images, from two different years, 2002 and 2007, in Setif city, Algeria. \nTo extract the required information, a combination hybrid method was developed, to introduce, firstly, a new visualizing approach of the formation and transformation of the urban form over time, which relies on the detection and thematic classification of urban fabrics through multi-scale and mathematical topologies; secondly, to introduce the allometric dimension through remote sensing classification to diagnose the morphological correlation of urban blocks.\nUsing MSVM code to classify pixels of this built-up area in two classes (concrete and tiled roofs) proposed in Marir, B. et al. (2018), this new method based on the entire modular support vector machine (MSVM) adopts the active learning machine (AL) method. We consider three different clustering algorithms (K-means, fuzzy c-means, and Gustafson-Kessel cluster). The classification accuracy was assessed from a set of samples selected by random stratification and from the second set of samples. To get more accuracy, the vectors are used in change detection subtraction of concrete and tiled roof targets, using land-cover change detection strategies (LCCD) suggested by ZhiYong (2021).\nIn post-processing, statistics are predicted using static allometry to ascertain the spatio-temporal variations in five years. The spectral analysis shows how urban changes form. The result, 0.24, of the allometric dimension is calculated from two scenes at two different times, which demonstrates that the tiled roofs are lower than the total average. This indicates that urban blocks in Setif city tend towards a new typology of buildings with other types of roofs with new materials, in particular concrete, according to rapid expansion and degrees of urban discontinuity.