Table 1.

Nomenclature.

s	midline coordinate, s ∈ [0,1]
ɛ(s)	elliptical cross section of fish body at s
a(s)	semi-major axis of cross section at s
b(s)	semi-minor axis of cross section at s
d(s)	displacement of cross section along normal axis at s
c	camera index, c = 1,2,3
f(s)	midline at s in body-fixed reference frame
S	the surface of a fish body
h	heading vector (orientation of head)
k	time index, k = 1,2, …
L	a line in three dimensions
m(s)	midline in world reference frame at s
cO	occluding contour in camera c
p	vector of polynomial coefficients
g	vertical axis in world frame
t(s)	tangent vector to the midline at s
x(s)	normal vector to the midline at s
y(s)	binormal vector to the midline at s
T	4×4 transformation matrix
cu	measurement in pixels in cth camera image
	projected estimate in pixels in cth camera image
Xk	state of a target at time k
Zk	measurements at time k
ℬ	body frame fixed to head
𝒞	camera reference frame
𝒲	world reference frame