How to iterate through a cell array and link elements in particle tracking?

Hi. I have tried several times to get this to work but I cant get my head around it, so any help is much appreciated.

I am trying to do some particle tracking across frame images. The output from the particle tracking is a cell array with the number of tracks made and the index to the row of the coordinate matrix where the particles are stored (Points matrix).

For example, Index_matrix{1} = [108; 0; 373] means that there are 3 frames (size of the track), but that on the second frame, the particle was not tracked but then was again picked up in the last frame. To get the coordinates of the points this track refers to, I would then index into the Points matrix for all tracks in a loop eg code below.

for u=1:Number_of_frames
    for i_track=1:size(Index_matrix,1)
        track_in=Index_matrix{i_track,:};
        track_points = (Points(track_in(u), :)); 
    end
end

I want to be able to plot the tracks on a per image basis, for example, for frame 1 I dont need to plot as its the first frame in the sequence. Frame 2, I would like to plot the tracks made from u=1 particles to u=2 particles. For frame 3, i would like to plot frame 2 - frame 3 for example. So I can do this with a change to code below track_points = (all_points(adj_track_inside(u-1:u), :));. But this actually fails with the example given above where there is a zero in the second frame, so if u=3, indexing with (u-1:u) wont work.

I also have to account for the occasion that Index_matrix{2} = [0; 0; 373] eg. particle only located in one frame

and Index_matrix{1} = [0; 108; 373] for example, where the particle track starts in second frame.

This is just an example of three frame tracks, but in theory it could be "n" frames. So i could be seeing tracks such as [103;0;25;0;29;38], and here my ideal scenario is I would plot 6 images: 1st image, no track (as its the 1st particle). 2nd image; no track(0 in track), 3rd image, draw the track connecting rows 103 and 25 so it would be u and u-2. 4th image no track (0 in track matrix), 5th image, draw the track connecting 29 to 25, so here it would be u and u-2 again here but the last image would be connecting consecutive tracks, so u and u-1.

I just cant seem to find a way to generalise this. Really sorry if this doesnt make sense.

I've attached my work in progess code below and the variables needed to make it run.

Thanks a lot!

%Input: Tracked particles per frame
% Index_matrix - cell array with number of rows == number of tracks made.
%zeros in the track means its not been picked up in this frame
%tracks has an old ID in there that I stored for later use and has NaNs in
%place of the 0s in the index matrix. I used this in the loop below so I
%could use logical 1,0 expressions. 

track_drawing=1;
full_frame=0;
all_points=vertcat(Points{:});
number_particles=size(Index_matrix,1); 
CM=jet(number_particles);
Number_of_frames=3;

if track_drawing
    if full_frame==0 %track particles that are missed in some frames but picked up in later frames
        
        for u=1:Number_of_frames    
                %read in image per frame and plot coordinates of the
                %particles - done 

             for m=1:number_particles

                     if u~=1 % There will be no tracks for the first frame. 

                          for j_track = 1 : number_particles   
                            
                            adj_track_inside = Index_matrix{j_track}; %Index of the points where tracks need to be made.
                            track_inside=tracks{j_track};
                            S=size(adj_track_inside,1);
                            tf=isnan(track_inside);
                            size_checking=adj_track_inside;                           
                            size_checking(size_checking==0,:)=[];

                                    if size(size_checking,1)==1
                                        disp 'no tracking' %only detected in one frame across all track so dont need to plot it. 
                                    else 
                                        if tf(u-1,1) ==1 ||  tf(u,1) ==1 %if theres a zero in that frame or in the frame before skip it. 
                                            continue
                                         
                                        elseif tf(u,1) ~=1 && tf(u-1,1)~=1
                                             track_points = (all_points(adj_track_inside(u-1:u), :)); 
                                        elseif tf(u,1) ~=1 && tf(u-1,1)==1
                                             track_points = (all_points(adj_track_inside(u-2:u-1), :)); 
                                        end
    
                                    hold on
                                    plot(track_points(:,1), track_points(:, 2), 'Color', CM(j_track,:),'LineWidth',3) 

                                    end
                          end

                     end 


                end     

    end

    end
end

no tracking
no tracking
no tracking
no tracking
no tracking
no tracking
no tracking
no tracking
no tracking
no tracking
no tracking
no tracking
no tracking
no tracking
no tracking
no tracking
no tracking
no tracking
no tracking
no tracking
no tracking
no tracking

[Ruby 19]

I should have added that whilst this code techincally works with no error messages, it is not correct. In attached variables, j_track = 108 and u=3 satisfies tf(u-1,1) ==1 || tf(u,1) ==1 where Index_matrix{108}= [108; 0; 373]. So here I instead need that the link can be made from the 3rd particle to the first, for u=3, where the particle in the 2nd frame is missing.

Answer 1

[dpb]

I don't have time at the moment to attack in earnest, but I'd probably start by simplifying and instead of trying to make it all work in one nested loop with deep logic, I'd first build a list of the frames found indices for each track, then process that list -- that eliminates the zero indexing. If there's not supposed to do anything between non-adjacent frames, then diff(indices)>1 will tell you that...

Index_matrix{1} = [108; 0; 373];
for i=1:numel(Index_matrix)
  indices=find(Index_matrix{i})     % which frames to process
  delta=diff(indices)               % the difference in frames vector
  for j=1:numel(delta)
      
  end
end

indices = 2×1

1 3

delta = 2

Answer 2

[Voss]

This plots using only the "good" (i.e., non-zero) indices from Index_matrix{jj}. Note that three additional particle tracks are plotted by this code vs by your original code, corresponding to the three particles that "disappeared" for a frame and then came back (particle #108, #115, and #122).

Based on your description of your ultimate goal (multiple images plotted), the code here doesn't get you there, but maybe it's a start. In any case, hopefully it's useful to see this simpler code that does what your code did (plus a little bit more).

load Index_matrix
load Points

all_points = vertcat(Points{:});
number_particles = size(Index_matrix,1); 
CM = jet(number_particles);

figure
hold on

for jj = 1:number_particles
    
    idx = Index_matrix{jj}; %Index of the points where tracks need to be made.
    
    is_good = idx ~= 0;
    
    if nnz(is_good) < 2
%         disp 'no tracking' %only detected in (at most) one frame across all track so dont need to plot it.
        continue
    end
    
    track_points = all_points(idx(is_good),:);
    
    plot(track_points(:,1), track_points(:, 2), 'Color', CM(jj,:),'LineWidth',3);
    
end

[dpb]

I hadn't seen OP's follow on that he wanted to plot between observations whether missing one (or more) inbetween or not--the diff() thing then isn't important and as you show, simply pulling the index vector gets the points...but I guess I don't follow that as compared to the description of "multiple images" which implies nothing is to be done for the frames that didn't track a given particle. It's not clear what "images" means here...a new figure with just a single (or no) trace on each so like could create a movie from, maybe? But then how to reconcile the comment of plotting from one observation to the next regardless of missing in between? 'Tis a conundrum indeed...

[Voss]

@dpb: I also wondered what exactly was the intended final output. @Ruby 19, can you clarify?

[Ruby 19]

Hi both,

Fistly thankyou so much for taking the time to help me. Both of your codes are much nicer to follow than mine. To clarify, I didnt put in the example images in the code for trying to streamline this example, but Image (u) where u indexes the number of frames i.e. the number of images, corresponds to an RGB image of the particles (generated by microscopy). I then have done a tracking code on the centers of mass of these particles in the RGB image (centers of mass = the Points matrix). In the final version of the code, I will load in these RGB images and display: for u=1 (Frame1) no tracks (just particle locations), u=2(Frame2), particle tracks detected from frame 1 particles to frame 2 particles....etc. With regards to the missing inbetween, its possible that a particle may disappear from one given frame, but it can be still detected in the next frame due to a linking distance in the tracking portion of my code (based on distance and expected trajectories).

Yes you are totally right that I am hoping to make a movie from this! :)

I should have left my figure section in - Apologies. It reads: and sits below the u loop. Hence in this simplified case of 3 frames, the expected output for the #115 particle would be 3 images where:

Index_matrix{115}=[115;0;382];

Image1 (u=1), has the co-ordinates of the #115 particle (no tracking for first frame.

Image2 (u=2), has nothing for this particle since Index_matrix{jj=2}==0, so the particle has no tracks and has not been detected here.

Image3 (u=3), has the coordinates of the #382 linked particle and the track made from u=1 to u=3.

Filename3=['imRGB_Frame', num2str(u),'.mat'];
            imRGB_data=load(Filename3);
            imRGB=imRGB_data.imRGB;
            figure     
            image(imRGB);

[dpb]

OK, what I had sorta' presumed. The way to do this is same idea as above excepting the use of the difference is now going to be important to flag empty frames.

The way to then build frames will be to not create a zillion files for each but to use im2frame to build the move struct in memory and then save it.

What's not clear to me from your statement is whether you want a single-particle movie for each particle individually, or whether all particles are to be shown...

[Ruby 19]

Thankyou for your reply and for pointing me to the im2frame option, I had not heard of this and I was planning on saving each image corresponding to each frame into a .Tiff and then building the movie outside of Matlab. So Thankyou!

I would need a movie where all particles and their tracks are shown at the same time, rather than a movie per particle.