Orientation estimation.

<p>(a) The illustration of Algorithm 1. Here <i>I</i>¹ and <i>I</i>² denote the image plane of <i>Camera 1</i> (blue) and <i>Camera 2</i> (red) respectively. The line-segment </p><p></p><p></p><p><mo stretchy="false">⟨</mo></p><p><mi>x</mi><mn>1</mn><mn>1</mn></p><mo>,</mo><p><mi>x</mi><mn>2</mn><mn>1</mn></p><mo stretchy="false">⟩</mo><p></p><p></p><p></p> (blue) denotes the ellipse’s major axis in <i>I</i>¹. And the line-segment <p></p><p></p><p><mo stretchy="false">⟨</mo></p><p><mi>x</mi><mn>1</mn><mn>2</mn></p><mo>,</mo><p><mi>x</mi><mn>2</mn><mn>2</mn></p><mo stretchy="false">⟩</mo><p></p><p></p><p></p> (red) denotes the ellipse’s major axis in <i>I</i>². The projection rays of those end-points define two plane Φ¹ and Φ² respectively, <i>e.g</i>. two blue rays define Φ¹. The orientation <i>O</i> is computed from the direction of the cross line (the longer green line) between two planes Φ¹ and Φ². Here all definitions are defined in the world coordinate system. (b) The orientation is problematic. The measurement is drawn in red, and red dashed lines are the major-axis and minor-axis of its ellipse. A generative shape according to the fly’s location <i>X</i> and orientation <i>O</i> is re-projected into the camera view (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0132101#pone.0132101.s002" target="_blank">S2 Fig</a> for the generative shape model.). The green pixels are re-projected pixels. Yellow pixels are identical pixels. (c) The error <i>ϵ</i> as a function of the ratio <i>γ</i>. Here <i>γ</i> defines the length ratio between the major-axis and the minor-axis of an ellipse.<p>