## 2 Related Work and the Proposed Algorithm
### Related Work
Algorithms of reconstruction depend principally on the system of vision (monocular, stereo, passive or active... ), the scene (indoor/outdoor, illumination... ), the input data, the application goals (pose estimation, tracking, mapping... ). Three dimensional shape reconstructions could be achieved using image shading, texture, photometric stereo, structured light, motion sequences, etc. In addition, reconstruction could be performed using image formation models and specific numerical techniques such as those presented in [23]. Early, shapes from stereo techniques in computer vision were tested on stereo image sequences [24] where a dense object reconstruction is obtained using iterative feature matching and shape reconstruction algorithms. The proposed algorithm resolves matching ambiguities by multiple hypothesis testing. Modern techniques use Delaunay triangulation algorithms for point cloud data with only geometric parameters as input since it have been shown to be quite effective both in theory and practice [25], although its long computational time when processing large data. It is also used in [6; 7; 23; 24] in addition with elastic surface-net algorithm [26] or the marching cubes algorithm [27] to extract mesh. [PERSON] presented in her work [28], a sparse disparity map reconstruction were produced based on features-based stereo matching technique from infrared images. A number of constraints (epipolar geometry) and assumptions (image brightness, proximity... ) are employed to retrieve matching ambiguities. A Delaunay triangulation algorithm is applied in order to reconstruct the scene, using disparity map information. In the case of underwater applications, water-glass-air interfaces between the sensor and the scene modify the intrinsic parameters of the camera and limit the standard image processing algorithms performances. Therefore, underwater image formation are studied and developed in [29; 30; 31] in order to incorporate properties of light refraction in water. The light refraction effects should be considered either when an underwater calibration is carried out [32; 33; 34] or during the 3D reconstruction algorithm [35]. The Refractive Stereo Ray Tracing (RSRT) process allows accurate scene reconstruction by modeling and tracing the refraction of the light. It is well suited for complex refraction through multiple interfaces; however this requires complete knowledge of the 3D projection process. This approach does not need an underwater calibration of the system of vision but the algorithm of light trajectory tracking is computationally time consuming particularly when there are multiple different environment between the 3D point and its 2D image projection. In contrast, underwater calibration, despite its experimentations ambiguities, provides a direct and simplified approximation between the merged 3D point and its 2D image correspondence as it takes into consideration light refraction effects in the expression of 2D-3D transformation. Several studies on 3D reconstruction systems are proposed in literature. However, few of them are designed for underwater application and fewer target real-time implementation. In Table 1, we summarize the main treatments and characteristics of some existing systems and those of our algorithm. The algorithms used for each case depend on multiples aspects: the 3D capturing sensor (passive/active, monocular/stereo, calibrated/non-calibrated... ), the points of interest that will be reconstructed (most interest points in all the image, specific key points, checkerboard corners... ), the application requirements (precision, software and hardware resources, timing... ), the system environment (aerial, underwater), etc. For example, the capturing sensor constitutions and configurations present a great interest to facilitate the image processing algorithms. For underwater applications, with the use of passive sensors [2; 36], the identification and recognition of object is tough and sometimes hopeless because of the underground homogenous texture and lack of illumination.