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22) where mat(·) is the function which converts the state vector into homography matrices and v(k) is the observation noise vector. It is assumed that the observation noise is Gaussian, it is not correlated with state noise, and its covariance matrix is R(k), which is computed by using first order noise propagation using Haralick’s Method [55]. 3. A potential observation is an image pair that has a potential overlapping area, as predicted by the state and its uncertainty. 4. An unsuccessful observation refers to the image pairs that were not successfully matched due to lack of overlapping area or failure of the registration algorithm.

2 Global Alignment When an underwater platform on which a down-looking camera is deployed revisits a previously surveyed area, it becomes essential to detect and match the non-time consecutive overlapping images in order to close a loop and, thus, improve the trajectory estimation. Let k−1 Hk denote the relative homography between the kth and (k − 1)th image in the sequence. The global projection of image k into the mosaic frame is denoted as 1 Hk and is called an absolute homography2. This homography can be calculated by composing the transformations 1 Hk = 1 H2 ·2 H3 · .

The total number of overlapping image pairs between key-frames is 150. This number later refined by choosing image pairs that have at least 20 percent of overlap. Final total number of overlapping image pairs is 85. Fig. 11(a) shows the initial estimation calculated by accumulation. 50 pixels computed over 32100 correspondences. If a feature has appeared in three or more images, it is added to the list of tracked features. The total number of tracked features is 1116 and their distribution with the images is given in Fig.

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