Fig 1.
Experimental set-up for 3D imaging.
A) Schematic showing the camera angles and 3D head-centred xyz coordinate frame. B) Horizontal and vertical views, with corresponding 2D coordinate frames.
Fig 2.
Description of whiskers by quadratic 3D Bezier curves.
Left: schematic of a 3D Bezier curve representing a whisker (blue line), defined by its three control points cp0,cp1 and cp2 (blue dots). Middle, right: projection of the 3D Bezier curve, and its control points, onto horizontal and vertical image planes.
Fig 3.
Left: Initialisation of control points for a given target whisker (see Methods for details). Initial values for control points in horizontal (top, white circles) and vertical views (bottom, white circles). White dotted lines in vertical view represent the range of z values consistent with each of the (x,y) points in horizontal view. Middle: Estimation of snout contour (yellow). Right: Fitting of 3D Bezier curves to image data. Projections of the 3D Bezier curve for one whisker (blue lines) and of its control points (blue dots) are shown in horizontal (top) and vertical (bottom) views. Yellow dots indicate intersections between snout contour and extrapolated Bezier curves.
Fig 4.
Tracking multiple whiskers in 3D.
A-B) 8 whiskers were tracked in a 3.5 s video sequence (1000 frames/s). C) A sequence of 12 frames showing Bezier curves for all tracked whiskers, projected into horizontal and vertical views, taken from the example video (S1 Movie). Whiskers are colour coded as in panel A. D) Tracking solutions for 2 whiskers (colour coded as in panel A) across 12 frames projected onto horizontal and vertical views. E) 3D tracking solutions for 8 whiskers across a sequence of 30 frames, including the sequence of panel D.
Fig 5.
Description of a whisker in terms of 3D kinematic and 3D shape parameters.
A) Azimuth (θ), elevation (φ) and roll (ζ) angles. These angles are defined with respect to the tangent to the Bezier curve b(s) describing the whisker, at s = 0. Azimuth describes rotation about the vertical (dorso-ventral) axis through s = 0; elevation describes rotation about the horizontal (anterior-posterior) axis through s = 0; roll describes rotation about the x′ axis, defined in panel B. B) Left. Whisker-centric coordinate frame with origin at s = 0 (Eqs 9–11). The x′ axis is tangent to b(s) at s = 0; the y′ axis is the direction in which b(s) curves; the z′ axis is orthogonal to the x′−y′ plane. Middle. Components of moment in the whisker-centric coordinate frame. Right. 2D and 3D whisker curvature (Eqs 13–15). rh and rv denote the radii of the circles that best fit the projection of b(s) into the horizontal and vertical image planes respectively (at a given point s); r3D denotes the radius of the circle that best fits b(s) itself.
Fig 6.
3D whisker kinematics during free whisking.
A) Changes in 3D angles for whiskers C1, C2 and C3 during a 3.5 s episode of free whisking. B) Relationships between angles.
Fig 7.
Tracking and estimating 3D curvature for a rigid test object (panels A-B), whiskers of a behaving mouse (panel C) and an ex vivo whisker (panels D-F). A) Tracking the edge of a coverslip. The coverslip was mounted, like a lollipop, on a rod; the rod was oriented in the mediolateral direction and rotated around its axis. Red lines indicate tracking results (30 frames, 10 millisecond intervals, 1000 frames/s). B) Top: Azimuth angle for two trials (black and grey traces). Bottom shows measured curvature: horizontal curvatures (dotted lines), κ3D (solid lines) and true curvature (orange). C) Horizontal and 3D curvatures during free whisking (same trial as Fig 6). Solid lines represent κ3D and dotted lines indicate horizontal curvatures for C1-3 (colours coded as in Fig 6). Fluctuations in vertical curvature were similar to those in horizontal curvature (|ρ|>0.49). D) Variation in κ3D for a stationary ex vivo whisker (C3) as a function of roll angle. E) Azimuth angle for ex vivo trials with simulated whisking at different speeds. F) κ3D as a function of whisking phase.
Fig 8.
Comparison of 2D and 3D curvature as mouse whisks against a pole (whisker C2): curvatures (upper panel)-, 3D kinematics (middle panel) and curvature change (bottom panel, Δκ3D, Δκh, and Δκv). A) Contact episode where both movement and bending of the whisker were largely restricted to the horizontal plane. In this case, Δκ3D and Δκh were highly correlated. Grey shading indicates periods of whisker-pole contact. See S3 Movie. B) Example with same whisker as panel A for contact episode with significant vertical component of whisker motion. See S4 Movie.
Table 1.
Parameters and variables summary.