**4.3 Performance analytics and originality**

To evaluate and measure the performance of our FPAK approach associated with the ARKit rendering engine, the results obtained are compared with two other approaches [64, 87, 93, 95] on the same basis of the five constraints referenced in **Table 2**.

The first comparison model is the Deterministic Simulated Annealing (DSA) metaheuristics optimization algorithm. In Pajares and Cruz [95], this strategy for stereovision matching was exploited with satisfactory results. It is a comprehensive approach belonging to the category of methods that incorporate explicit smoothing assumptions and determine all disparities simultaneously by applying a energy minimization process. The limits of this approach are felt when the input database exceeds 82 pairs of stereo images and whose convergence is only reached after 30 iterations [87].

The second comparison model is based on the so-called relaxation labeling approach (RELB). This is a technique proposed by Rosenfeld et al. [98] to account for uncertainty in sensory data interpretation systems and to find the best matches. It uses contextual information as an aid to the classification of a set of interrelated objects by allowing interactions between possible classifications of related objects. In the stereovision paradigm, the problem is to assign unique labels (or matches) to a set of features in an image from a given list of possible matches.

The objective is to assign to each feature (edge segment) a value corresponding to the disparity in a way consistent with certain predefined constraints according to probabilities assigned to the five constraints in the studies [64, 93]. Here, the maximum number of input image pairs is increased to 90 for convergence from the 35th iteration. The results of performance comparison are synthetized in **Table 4**.

Although pioneering works [64, 87, 93, 95] have paved the way for the fuzzy modeling of the constraints inherent in image matching in stereovision applications, the originality of our work is assessed at three distinct levels. First, our method fits perfectly with a professional rendering engine such as ARKit. Second, the five constraints are modeled as concepts within the framework of FCMs. And third, the calculations did not require additional models as in the case of the DSA or RELB based approach. In doing so, the entire modeling chain constituted a fuzzy inference system.
