How do I use 'pcolor' with adaptive bin widths?

I have a grey scale image of dimensions 600x600.

basically I want to to create a histogram of each row (with adaptive bin width), of the image. The problem is; I want to combine these histograms into one large visualization that has the same size as the original image - that is, the visualization should also contain 600 rows. I expected I could use the build in 'pcolor' Matlab function for this, where the color of a 2d 'bin' would correspond to the number of occurrences of that 'itensity' in that row. However, since the matrix dimensions of the X and Y parameter to 'pcolor' must agree with the original image (600x600), I don't see how I can have e.g. one 'histogram row' contain 5 bins, but the next one e.g. 9.

I have tried to visualize what I want as the final output below.

Please do not consider the colors I have chosen as important the least bit, they should only signify high and low intensities densities - e.g. redish colors = a lot of itensities, blueish colors = few number of intensities.

My follow up question is then; how to I expand this, so that the rows can also have an adaptive width? Again to visualize:

The real problem with these two questions is the visualization part, not anything related to the histograms.

Kind regards Jacob