| Axes |
| x |
Anterior-posterior axis, with positive posterior |
| y |
Medio-lateral axis, with positive medial |
| z |
Dorsal-ventral axis, with positive dorsal |
| v |
Medio-lateral axis from the vertical view, with positive medial |
| w |
Dorsal-ventral axis from the vertical view, with positive ventral |
|
x′ |
Axis of the whisker centred coordinated frame described as tangent to the whisker at s = 0. Positive indicates toward the tip of the whisker. |
|
y′ |
Axis of the whisker centred coordinated frame defined by the second derivative of the Bezier curve at s = 0. Positive indicates s>0 |
|
z′ |
Axis of the whisker centred coordinated frame defined as the cross product between x′ and y′ |
| Calibration |
|
pH
|
Point in the horizontal plane with coefficients (x,y)T
|
| H |
Matrix related to mapping between p3D and pH. [1 0 0; 0 1 0] |
|
p3D
|
Point with coefficients (x,y,z)T
|
| h |
Vector related to the mapping between p3D and pH. |
|
pV
|
Point in the horizontal plane with coefficients (v,w)T
|
| V |
Matrix related to mapping between p3D and pV. Values of V are fitted during the calibration procedure |
| v |
Vector related to the mapping between p3D and pV.Values of v are fitted during the calibration procedure |
| Bezier curves and fitting process |
|
b(s) |
Bezier curve evaluated at s where 0≤s≤1 |
|
cpi
|
Control point i = 0,1,2 with coordinates (x,y,z)T
|
| j |
whisker |
| f |
frame |
|
Ev(j) |
Term from objective function (Eq 4) related to vertical image |
|
Eh(f) |
Term from objective function related to horizontal image |
|
Ih(x,y) |
Intensity at the point (x,y) in the horizontal image |
|
Iv(v,w) |
Intensity at the point (v,w) in the horizontal image |
|
R1
|
Regularising term from the objective function related to temporal contiguity |
|
R2
|
Regularising term from the objective function related to shape complexity |
|
σ1
|
Selectable parameter that weights the first regularising factor R1
|
|
σ2
|
Selectable parameter that weights the second regularising factor R2
|
| q |
Vector related to Eq 8. |
| Extraction of kinematic parameters |
| i′ |
Unit vector that point in the direction of x′ |
| j′ |
Unit vector that point in the direction of y′ |
| k′ |
Unit vector that point in the direction of z′ |
| ζ |
Rotation angle of the whisker respect to x′ |
| θ |
Azimuth angle defined as the angle between the x axis and the projection of tangent at the base of the whisker in the horizontal plane |
| φ |
Elevation angle defined as the angle between the -z axis and the projection of tangent at the base of the whisker in the vertical image |
| κ3D(s) |
3D Curvature evaluated at s
|
| κh(s) |
Curvature of the projection of the Bezier curve in the horizontal plane evaluated at s
|
| κv(s) |
Curvature of the projection of the Bezier curve in the vertical image evaluated at s
|
