We present a new minimal problem for relative pose estimation mixing point features with lines incident at points observed in three views and its efficient homotopy continuation solver. We demonstrate the generality of the approach by analyzing and solving an additional problem with mixed point and line correspondences in three views. The minimal problems include correspondences of (i) three points and one line and (ii) three points and two lines through two of the points which is reported and analyzed here for the first time. These are difficult to solve, as they have 216 and -as shown here -312 solutions, but cover important practical situations when line and point features appear together, e.g., in urban scenes or when observing curves. We demonstrate that even such difficult problems can be solved robustly using a suitable homotopy continuation technique and we provide an implementation optimized for minimal problems that can be integrated into engineering applications. Our simulated and real experiments demonstrate our solvers in the camera geometry computation task in structure from motion. We show that new solvers allow for reconstructing challenging scenes where the standard two-view initialization of structure from motion fails.

In this paper we introduce a general framework for analyzing the numerical conditioning of minimal problems in multiple view geometry, using tools from computational algebra and Riemannian geometry. Special motivation comes from the fact that relative pose estimation, based on standard 5-point or 7-point Random Sample Consensus (RANSAC) algorithms, can fail even when no outliers are present and there is enough data to support a hypothesis. We argue that these cases arise due to the intrinsic instability of the 5-and 7-point minimal problems. We apply our framework to characterize the instabilities, both in terms of the world scenes that lead to infinite condition number, and directly in terms of ill-conditioned image data. The approach produces computational tests for assessing the condition number before solving the minimal problem. Lastly synthetic and real data experiments suggest that RANSAC serves not only to remove outliers, but also to select for well-conditioned image data, as predicted by our theory.

For multifocus image fusion in spatial domain, sharper blocks from different source images are selected to fuse a new image. Block size significantly affects the fusion results and a fixed block size is not applicable in various multifocus images. In this paper, a novel multifocus image fusion algorithm using biogeography-based optimization is proposed to obtain the optimal block size. The sharper blocks of each source image are first selected by sum modified Laplacian and morphological filter to contain an initial fused image. Then, the proposed algorithm uses the migration and mutation operation of biogeography-based optimization to search the optimal block size according to the fitness function in respect of spatial frequency. The chaotic search is adopted during iteration to improve optimization precision. The final fused image is constructed based on the optimal block size. Experimental results demonstrate that the proposed algorithm has good quantitative and visual evaluations.

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