**1. Introduction**

The use of advanced scientific computation methods and techniques is classic in geography, land use and regional planning [1–8]. Indeed, the study and analysis of geographical spaces such as cities for example, which themselves have acquired the qualification of complex system [1, 2, 5, 9–14] are an illustration of this classic usage [15–24]. Among these scientific computational approaches is also fuzzy inference logic [21, 22, 25, 26]. As part of the research work reported in this chapter, we relied on the scientific achievements of fuzzy inference systems [27–30] to integrate into our methodological approach Fuzzy Cognitive Maps (FCM) [31–34] in the process of

visual features matching computation. It's applied through the collection of captured photography of urban built environment to build an augmented urban reality model [35–40].

Thereby, thematic analyzes of built urban environments require the acquisition of 3D urban landscape data, street furniture and several other real visual data. The data to be processed are bi-dimensional (2D) images captured from the tri-dimensional (3D) scene. The objects in 3D are generally composed of related parts that joined from the whole object. In computer graphics, we usually use a specialized software, for instance, Maya [41] or Blender [42, 43] to interactively create models or procedural 3D modeling [44–48] which creates a mathematical representation of a 3D object. It is common to use a few photographs as references and textures to generate models using a modeling tool. When it comes to 3D modeling and urban spaces [49–51], the more systematic introduction of photographs as input to generate a photorealistic 3D model of a built environment is called « Image-based Modeling" [52] and can generate models for objects physically existing. More importantly, such a modeling process can be automated, and therefore can be scaled up for applications [52]. More fundamentally, how to recover the lost third dimension of objects from a collection of 2D images is one of the main objectives of computer vision [53] and the technical challenge resolved in this work. Fortunately, the relations in 3D are preserved in 2D [42, 44, 45, 47, 54]. Hence, we can exploit this fact by considering specific and basic elements which are related to other elements in the 2D images. Those specific and basic elements are stereo correspondence features: epipolar [55], similarity [56], smoothness [57], ordering [58] and uniqueness [59].

Indeed, the use of photogrammetry, which is a technique that consists of taking measurements in a scene, using the parallax obtained between images acquired from different points of view, proves to be an excellent approach for producing captures that conform to the reality [53]. To better manage the parallax during the 3D reconstruction, we combined fuzzy classification algorithm [8, 60, 61] to the photogrammetric processing within the framework of the well-established soft computing technique called Fuzzy Cognitive Map (FCM) [62–67]. Our Fuzzy Photogrammetric Algorithm Kernel (FPAK) applied to 3D reconstruction from images precisely becomes the meeting point of computer graphics and vision, with the finalized 3D representation of urban built environment.

The rest of the chapter is organized as follows: Section 2 presents background of FCM and its mathematical formalization we adopted [22]. Section 3 expose the core of this chapter: materials and methods. Section 4 presents with the experimental results obtained. The conclusion of the chapter puts lights on the future.
