A mathematichal model for interpretation for images under uncertainties in different fields

Real-world objects, in many fields of investigations, are mapped to the digital raster image through a variety of sensors, making the image only an approxi-mation to the real-world object. Due to imperfections in either the image data or the edge detector, there may be missing points or pixels on lines as well as spatial deviations between ideal line and the set of imprecise points obtained from the edge detector. The overall effect is an image that has some distortion in its geometry. It is introduced a mathematical model based on linear fuzzy space, which cover these uncertainties and helps in the correct interpretation and important decisions in different fields: image analysis (imprecise feature extraction), GIS (imprecise spatial object modeling), robotics (environment models), and in medicine (DICOM medical images).