Measuring rainbow trout by using simple statistics - Emerging Trends in Image Processing, Computer Vision, and Pattern Recognition - page 35

the trout. Its high is proportional to the canalization base length to avoid extra data to be cap-
tured.
3 Statistical Measuring Approach
In this section, we present our statistical approach to measure rainbow trout.
Considering the rainbow trout natural swimming movement against the water flow and ob-
serving the trout from a downward point of view, we hypothesized that a third- order curve
could approximate the trout's body within the water.
Diferent procedures can be followed to obtain a third-order curve equation. However, we
prefer a simple but effective solution that could be executed online after a trout's image is cap-
tured.
Then, given n sample points ( x , y ) which depict the trout body, we apply minimum squares
to compute a polynomial third-order equation [ 14 ] :
(1)
where a 0 , a 1 , a 2 , a 3 are constants that gain their values by solving the [4 × 4] equation system (2) :
(2)
The equation system (2) can be easily solved using the matrix notation, AX = B , or more spe-
ciically: X = BA − 1 .
After this computation, we obtained the best regression curve that adjusts the trout's body
captured into an RGB image.