Python - Finding the linear equation of a line in a image

Question

I am using Python v2.7 for this work. As an input i have a relatively white image with a clear black line on it. The line is always linear, no polynomial of second or above order. The line can be anyway on the image

I am trying to define the equation of this line in the form of y = ax +b

Currently my approach would be to find which pixel belongs to the line then do a linear regression to get the equation. But i am trying to find out which function in python i need to use to achieve this and this is where I would need some help

Or maybe you have an even simpler way of doing it.

adding one image as example

Answer 1

Okay so i found the way i wanted to do quite simply in the end

def estimate_coef(x, y): 
    # number of observations/points 
    n = np.size(x) 

    # mean of x and y vector 
    m_x, m_y = np.mean(x), np.mean(y) 

    # calculating cross-deviation and deviation about x 
    SS_xy = np.sum(y*x) - n*m_y*m_x 
    SS_xx = np.sum(x*x) - n*m_x*m_x 

    # calculating regression coefficients 
    a = SS_xy / SS_xx 
    b = m_y - a*m_x 

    return(a, b) 


# MAIN CODE
# 1. Read image
# 2. find where the pixel belonging to the line are located
# 3. perform linear regression to get coeff

image = []      # contain the image read

# for all images to analyze
for x in range(len(dut.images)):
  print "\n\nimage ",x, dut.images[x]

  # read image (convert to greyscale)
  image  = imread(dut.images[x], mode="L")

  height = image.shape[0] - 1

  threshold = (np.min(image) + np.max(image)) / 2
  line = np.where(image < threshold) #get coordinate of the pixel belonging to the line

  x = line[1] # store the x position
  y = height - line[0] # store the y position. Need to invert because of image origine being on top left corner instead of bottom left

  #position = np.array([x,y])

  a, b = estimate_coef(x, y)
  print("Estimated coefficients:\n \
       a = %.6f \n \
       b = %.6f" % (a, b))