Automatically align image and graph with shared x-axis

Question

I have an image that I want to plot under a graph showing the intensity of an arbitrary row of this image.

Apparently, there is no way I can "automatically" make the two graphs both aligned (they share the same x-axis) and not distorted.

Here is a MWE that uses the kobi.png image that should come with MATLAB. For this solution I used the answer to this question, but it's not exactly what I am looking for. The reason will be clear after the code.

im = imread('kobi.png'); % read default image
img = rgb2gray(im); % convert to grayscale

y = 600; % select line to "scan"

% plot image with highlithed line
subplot(3,3,4:9);
imagesc(img);
colormap gray
hold on
line([0 size(img,2)], [y y], 'Color', 'r', 'LineWidth', 1.5);
hold off
axis image

photoAxs = gca;
photoAxsRatio = get(photoAxs,'PlotBoxAspectRatio');

% plot intensity of selected row
subplot(3,3,1:3);
r = img(y, :);
plot(r);
axis tight

topAxs = gca;

% adjust ratios
topAxsRatio = photoAxsRatio;
topAxsRatio(2) = photoAxsRatio(2)/2.4; % I want to get rid of this number!  
set(topAxs,'PlotBoxAspectRatio', topAxsRatio)

As you can see, this produces (almost) the expected result, but there is an hardcoded number (that in the answer I linked was different, 3.8, while here is 2.4), that I would like to eliminate. Also, I think this number gives only an apparently aligned solution, but with my slight OCD this room for error gives me the creeps!

So the question is:

Is there any viable way to automatically align a graph and an image that have the same x-axis while maintaining the image aspect ratio?

Calle

Answer 1

Old code:

topAxsRatio = photoAxsRatio;
topAxsRatio(2) = photoAxsRatio(2)/2.4; % I want to get rid of this number!  
set(topAxs,'PlotBoxAspectRatio', topAxsRatio)

New code:

photoratio = photoAxs.PlotBoxAspectRatio(1)/photoAxs.PlotBoxAspectRatio(2);
ratio = photoratio * photoAxs.Position(4)/topAxs.Position(4);
topAxs.PlotBoxAspectRatio = [ratio, 1, 1];

Result:

---

A bit of explanation:

When figures are first plotted, you will notice only the heights are different, although you can clearly see the widths are also different.

I'm not 100% sure the reason Matlab does this, but this is my guess.

Usually, two properties, width and height, are sufficient to define the size of a 2D figure, but Matlab introduces an extra property, PlotBoxAspectRatio, to control the size. To avoid conflict, Matlab decides to give the width property a fixed number when a figure is first created. However, the actual width is calculated by height*PlotBoxAspectRatio.

Therefore, we have:

TopAxis.width = TopAxis.height * TopAxis.ratio 
Photo.width = Photo.height * Photo.ratio

In order to preserve the initial height of the TopAxis, we can only change the aspect ratio.

Let

TopAxis.width = Photo.width

We have

TopAxis.height * TopAxis.ratio = Photo.height * Photo.ratio
TopAixs.ratio = Photo.ratio * Photo.height / TopAxis.height

And the Matlab code equivalent is the new code proposed.

Inaction

Thank you! Your explanation is excellent, and it explains that 2.4 (that was actually correct). It is the ratio between the heights of the two figures, isn't it? :) – Calle

@Calle Indeed, I didn't realise that :D – Inaction