Measuring shift between two images along one direction only

Question

I have to measure shifts between two monochromatic images.

These images are actually spectra before calibration, which are very noisy and full of unwanted features, but they basically look like following

I know that between different images, they have shifts along x-direction, but not along y-direction. And I want to know the amount of the shift along x-direction between them.

Luckily I found a function in skimage, register_translation, which can be used for arbitrary subpixel precision. But the problem is, I want to know shift along x-direction only, and I want resulting y-direction shift to be 0, but the program finds the shift to x and y at the same time, presumably along the direction perpendicular to the features. (marked as blue arrow in the figure)

So, I am wondering :

1. is there any function or package in python that measures the shift between two images along one direction only, or even with any prior knowledge?

2. what is a correct way of finding shifts between two noisy images? Would finding maximum cross-correlation value in FFT space would do the job?

Answer 1

I'm not positive it will work, but: one of the benefits of open source is that you can look at the implementation details of register_translation, then try to adapt it to your case. In your case, I would replace the fftn with fftn(..., axis=1), so that you only compute the fft along the columns axis. Then, multiply the two FFT signals together (this is equivalent to the convolution of each line, as suggested by @CypherX). Finally, you have to find a way to "coalesce" the shifts found along each line into a single measurement. One idea would be to take each shift (the maximum along that line) and plot a histogram. One would hope that you get a sharp peak around the true x shift.

If it works, it would be a pretty great contribution to scikit-image to add an "axis" keyword argument to register_translation. You can read the how to contribute guide and propose a change accordingly!

Answer 2

Some simple maths should do in this situation if register_translation gives you the xy shift, be it in vector or component form. You can calculate the movement in x that would be required if the y shift was non-existent, which is what you want. I am travelling so unfortunately can't give you the graph right now, would recommend drawing the triangles out.

The extra x shift required (x_extra) is defined by:

x_extra = y * tan[arctan(y_shift/x_shift)]

Which is simplified to:

x_extra = y_shift^2 / x_shift

Therefore, the total shift in x is:

x_shift_total = x_shift + x_extra

Where the x_shift is given to you by register_translation.

If you then move imageA by x_shift_total, it should be aligned with imageB, assuming the x_shift given by register_translation is correct.

@jni I would be keen to implement this as an option in register_translation!

Answer 3

Another, much faster and simpler, approach would be to calculate the horizontal profile at the same location in both images. That would give you a 1D profile for each image horizontally. Simple peak finding will then give you the location of the lines, and the difference between the peak indexes will tell you the shift solely in the x-axis.

I use this approach routinely to do shift detection similar to your problem, and it is very very fast, very simple, and very robust.

# pick a row to use
row = 10
x_profile1 = np.mean(image1[row, :], axis=0)
x_profiel2 = np.mean(image2[row, :], axis=0)

# 'get_peaks' is a function to return indices of found peaks - several
# around
peaks1 = get_peaks(x_profile1)
peaks2 = get_peaks(x_profile2)

x_shift = peaks1[0] - peaks2[0]

Answer 4

Method-1

You could use convolution between the two images to find where you get a maximum. You could envision this as sliding the non-shifted images over the shifted image from left to right, and the convolution will produce maxima corresponding to the scenario when the identical sections of each image lies on top of one-another. Take a look at scipy.ndimage.convolution and scipy.signal.convolve and see which one suits your needs better.

Method-2

1. On the other hand, you could take a horizontal slice from each image and find the position of the peaks (assuming black strips are 1's and white regions are 0's).
2. Calculate the centroids of these peaks in each image. Find the difference between the positions of these centroids and that is the shift your are looking for.
3. For robustness, you could then apply this to various rows of the image-pairs and the average of all the such differences would be a more statistically viable result for a measure of horizontal shift.