Mixed Signature: An Invariant Descriptor for 3D Motion Trajectory Perception and Recognition

<table>The subcoordinates of the mirror symmetrical motion trajectory. (a) is <svg height="16.450001" id="M81" style="vertical-align:-3.39066pt" version="1.1" viewbox="0 0 29.3125 16.450001" width="29.3125" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,12.162)"><path d="M480 416q0 -21 -18 -41q-9 -11 -17 -7q-20 9 -42 9q-62 0 -140 -78q23 -69 88 -192q17 -31 27 -42t20 -11q16 0 62 46l17 -20q-64 -92 -119 -92q-35 0 -70 66q-41 73 -84 187q-36 -30 -62 -61q-27 -115 -35 -172q-41 -8 -78 -20l-6 6l140 612q7 28 0.5 34t-37.5 7l-34 1
l5 26q38 4 74 13.5t57 17t25 7.5q12 0 4 -32l-104 -443h2q35 38 97 93q39 35 65.5 56t62 41.5t58.5 20.5q19 0 30.5 -10t11.5 -22z" id="x1D458"></path></g><g transform="matrix(.017,-0,0,-.017,8.613,12.162)"><path d="M368 703l-264 -866h-60l265 866h59z" id="x2F"></path></g><g transform="matrix(.017,-0,0,-.017,15.616,12.162)"><use xlink:href="#x1D458"></use></g>
<g transform="matrix(.012,-0,0,-.012,24.162,16.25)"><use xlink:href="#x1D460"></use></g>
</svg> and (b) is <svg height="16.299999" id="M82" style="vertical-align:-3.39066pt" version="1.1" viewbox="0 0 28.637501 16.299999" width="28.637501" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,12.013)"><path d="M471 456q-22 -60 -37 -85q-20 -3 -84 -3q-9 0 -29 2t-29 2q-38 -145 -54 -234q-15 -80 14 -80q23 0 68 38l14 -25q-78 -83 -137 -83q-50 0 -50 64q0 25 7 57l67 266q-57 4 -98 -9t-80 -49l-20 21q14 18 27 31t36.5 30t56.5 26t73 9q26 0 82.5 -2t89.5 -2q21 0 32 5t24 24
z" id="x1D70F"></path></g><g transform="matrix(.017,-0,0,-.017,8.273,12.013)"><use xlink:href="#x2F"></use></g><g transform="matrix(.017,-0,0,-.017,15.276,12.013)"><use xlink:href="#x1D70F"></use></g>
<g transform="matrix(.012,-0,0,-.012,23.487,16.088)"><use xlink:href="#x1D460"></use></g>
</svg>.</table>

Mathematical Problems in Engineering

fig9

Figure 9

Figure 9: Mixed Signature: An Invariant Descriptor for 3D Motion Trajectory Perception and Recognition 