Line-Based Multi-Label Energy Optimization for Fisheye Image Rectification and Calibration - Supplementary Material

This document shows the details on Multi-Label Energy Optimization (MLEO) method used for circular arcs selection and additional results for Line-Based Multi-Label Energy Optimization for Fisheye Image Rectification and Calibration, described in the submitted manuscript (CVPR submission 1687). The Structure of this document is as follows: • The next section describes details about the relationship between our circular arcs selection function and the MultiLabel Energy Optimization (MLEO) method. Our proposed function can be seen as a specific case for MLEO function presented in the manuscript. • Figure 1 provides the graph cut like relationship of our circular arcs selection method and MLEO method. • Figure 2 shows more experimental results for circular arcs selection algorithm. • Figure 3, 4 and 5depict additional successfully rectified results for images download from Internet. • Figure 6 and Figure 7 illustrate the results for synthetic approach where the images is captured by the same fisheye camera • Table 1 demonstrates our synthetic results of intrinsic parameters for Figure 7 and the result of existed approach using chessboard. • Figure 8 and Figure 9 display the failed examples of proposed algorithm. For the rectified examples of Internet images illustrated in the following, the first row is the source image download from Internet, the second row is the clustered circular arcs using our proposed algorithm and and the last row always depicts corresponding rectified results. In our experiments, the initial value of LM algorithm for line-based fisheye image rectification is as follow: