Approximation of a functional curve in a digital image
Adapted from a Mathcad Advisor file by Marco Asmad. Also see https://community.ptc.com/t5/PTC-Mathcad/Extract-data-from-chart/m-p/165695 by RichardJ.
We start with the curve image in gray scale:
Yellow boxes are the places where you can modify the values for scan your own curve.
Use this also
and make a validation of the data computing the average value of each row and column, then compares this value with kline which has represents the gray value selected to define the maximum "black" pixel.
Try for different kl values until find a good one.
Cleaned data
Original data
Shorthand for boxes:
With the matrix cleaned we can look for pixels from the function curve. With the following function we can scan the cleaned image matrix in the vertical and horizontal directions to find pixels that belong to the curve; the maximum opaque color is contained in the variable kcurve.
Try for different kc values until find a good one.
Also isolate the curves selectring adequate ranges for torque, power and speed
Read range values here
and the same true values for the boxes here
Scanned data
Original data
Now we convert into img coordinates:
Shorthand for interpolation:
Shorthand for plots:
This scale the scanned values
Now average the set of Y values at each X value to define the final data points, then to fit a curve with only N points.
Choosing some few points we get
So, this two matrices it's all we need for reconstruct both curves