Decomposition of free swimming zebrafish larval backbone shapes into orthonormal basis.

<p>(A) Still images of a swim bout from a representative movie of free swimming zebrafish larva, recorded at 500 fps. (B) Spline fit of fish backbone (cyan). Tangent vectors (black arrow) at 10 evenly spaced segments along the backbone from head (<i>s</i>₀ = 0) to tail (<i>s</i>₉ = 9) point along a direction <i>θ</i>(<i>s</i>_<i>j</i>). (C) Swim bout from A parameterized by Δ<i>θ</i>(<i>s</i>_<i>j</i>,<i>t</i>_<i>i</i>) = <i>θ</i>(<i>s</i>_<i>j</i>,<i>t</i>_<i>i</i>)–<i>θ</i>(0,<i>t</i>_<i>i</i>). (D) Singular value decomposition of Δ<i>θ</i> into eigenshapes <i>V</i>_<i>k</i>(<i>s</i>_<i>j</i>) (<i>j</i> = 1, 2… 9), the first three of which are plotted (red, blue, and green, respectively). The light colors correspond to eigenshapes determined from analyzing individual fish from a population, and dark colors are the collective eigenshapes from analyzing the entire population at once. (E) Bar plot of % weights (<math><mrow><msub><mi>S</mi><mrow><mi>k</mi><mi>k</mi></mrow></msub><mo>/</mo><mo>∑</mo><mrow><mi>k</mi><mo>′</mo><mo>=</mo><mn>1</mn></mrow><mrow><mn>10</mn></mrow><mrow><msub><mi>S</mi><mrow><mi>k</mi><mo>′</mo><mi>k</mi><mo>′</mo></mrow></msub></mrow></mrow></math>, where <i>S</i>_<i>kk</i> are the singular values) of each eigenfunction <i>V</i>_<i>k</i>(<i>s</i>_<i>j</i>). The right axis in cyan shows the cumulative contribution of each eigenshape. The first three eigenshapes contribute 96% of the total variance in Δ<i>θ</i>.