Algebraic and Geometric Topology, Part 1 by Milgram R. (ed.)

By Milgram R. (ed.)

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Example text

From the table and the resulting mosaics, it can be seen that both Capel’s method and the proposed method have caused some distortions on the image size, which is mainly because of the initial estimation. Moreover, in Fig. 9(b), it can be seen that images which are in the outer transects suffer from higher distortion than those located in the inner transects in order to become better aligned. 000 (a) (d) (b) (c) (e) Fig. 9 (a) Resulting mosaic of Capel’s method. (b)Resulting mosaic of the proposed method.

The main advantage of using this method to calculate the optimal path is that the homographies are less affected by accumulation errors. For global alignment the error function is defined over a set of grid points on the mosaic. 31) 22 2 Feature-Based Image Mosaicing where n is the total number of edges between images that contain grid point xk and Hi , H j denote absolute homographies. 32) i where m is the total number of grid points. Although this strategy has the advantage of distributing the errors, it has some disadvantages, such as: (1) point locations must be chosen very carefully so that every image and overlapping area has enough grid points to calculate the homography, and (2) since the detected feature points are distributed arbitrarily, they may fall in a textureless area, making it difficult to match them in another image.

For closed loop sequences, the total number of relative homographies is greater than the total number of images. 2, which are simple and easy to implement. However, an adequate parameterisation is not used on these elements to take advantage of the special structure of rotation-induced homography. This leads to over parameterisation which might cause overfitting. Szeliski et al. 24) 2 where k and m are images that have an overlapping area and n is the total number of correspondences between the images.

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