image analysis curve fitting

curve-fitting, image-processing, python

Solution

I saved your image to a file `14154233_input.png`. Then this program

import pylab as plt
import numpy as np

# Read image from disk and filter all grayscale
im = plt.imread("14154233_input.png")[:,:,:3]
im -= im.mean(axis=2).reshape(im.shape[0], im.shape[1], 1).repeat(3,axis=2)
im_maxnorm = im.max(axis=2)

# Find y-position of remaining line
ypos = np.ones((im.shape[1])) * np.nan
for i in range(im_maxnorm.shape[1]):
    if im_maxnorm[:,i].max()<0.01:
        continue
    ypos[i] = np.argmax(im_maxnorm[:,i])

# Pick only values that are set
ys = 1-ypos[np.isfinite(ypos)]
# Normalize to 0,1
ys -= ys.min()
ys /= ys.max()

# Create x values
xs = np.linspace(0,1,ys.shape[0])

# Create plot of both 
# read and filtered image and
# data extracted
plt.figure(figsize=(4,8))
plt.subplot(211)
plt.imshow(im_maxnorm)
plt.subplot(212, aspect="equal")
plt.plot(xs,ys)
plt.show()

Produces this plot:

You can then do with `xs` and `ys` whatever you want. Maybe you should put this code in a function that returns xs and ys or so.

One could improve the precision by fitting gaussians on each column or so. If you really need it, tell me.

Problem

I have a bunch of images like this one: The corresponding data is not available. I need to automatically retrieve about 100 points (regularly x-spaced) on the blue curve. All curves are very similar, so I need at least 1 pixel precision, but sub-pixel would be preferred. The good news is all curves start from 0,0 and end at 1,1, so we may forget about the grid. Any hint on Python libs that could help or any other approach ? Thanks !

Original source