{"id":1968,"date":"2014-02-05T17:32:44","date_gmt":"2014-02-05T17:32:44","guid":{"rendered":"https:\/\/www.anagram.at\/en\/diplomarbeit\/search-for-corresponding-lines\/"},"modified":"2014-02-05T17:32:44","modified_gmt":"2014-02-05T17:32:44","slug":"search-for-corresponding-lines","status":"publish","type":"page","link":"https:\/\/www.anagram.at\/en\/diplomarbeit\/search-for-corresponding-lines\/","title":{"rendered":"Search for corresponding lines"},"content":{"rendered":"


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\n Next:<\/b> Object detection<\/a>
\n Up:<\/b> Correspondence Analysis<\/a>
\n Previous:<\/b> Correspondence Analysis<\/a>
\n<\/p>\n

<\/p>\n

Search for corresponding lines
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\nAfter the line lists for both images are generated, the correspondence problem<\/i> needs to be solved. In contrast to an intensity-based correspondence analysis, there is no need to have a maximum disparity limit because all the lines are compared and thus all possible disparities are taken into consideration. But a constraint, that a line which is nearer than another is more likely to be chosen than a line which is more far away, has to be inserted. This constraint is needed, because if there are two objects mapped with approximately the same y-coordinate and approximately the same line properties, e.g. the same length, attitude and midpoint, as it is if two robots are next to each other, the left border of the robot could be matched with the left border of the other robot. Figure 3.12<\/a> depicts this situation.<\/p>\n

<\/p>\n\n\n
Figure 3.12:<\/strong>
\nLine ambiguity, the left image shows the merged original images (the alpha value of the right image has been decreased) and the right image shows the line ambiguity if no constraint is inserted<\/caption>\n
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\n <\/div>\n<\/td>\n<\/tr>\n<\/table>\n<\/div>\n

To avoid matching of two opposite lines, the gradient direction is taken into consideration. Figure 3.12<\/a> shows the gradient direction for the left edge image (depicted as red arrows in the electronic version of this thesis at the top and bottom). To measure the similarity between two lines, the weighted sum of the difference between the attitude \"$ , the direction \"$, the length \"$ and the difference in the y-coordinate between the start and end point \"$ of the line is computed. Let \"$ denote a line inside the right image, then the rating \"$ of a line \"$ can be formulated as<\/p>\n\n

<\/p>\n\n\n
\"$displaystyle<\/td>\n\n(3.15)<\/td>\n<\/tr>\n<\/table>\n<\/div>\n


<\/p>\n\nwhere \"$,
\n\"$, \"$ and
\n\"$ are weights, that define the importance of the line property. The currently implemented method uses
\n\"$ as \"$.
\nA line \"$ corresponds to a line \"$, if<\/p>\n