Matlab implementation of light speed labeling

Question

I am trying to implement code for the light speed labeling technique described in this article (I cannot use the Image Processing Toolbox): https://pdfs.semanticscholar.org/ef31/7c257603004d818ca1e2a2aa67d36d40147e.pdf (see section 2, page 7).

Here is my Matlab code for LSL equivalence construction (algorithm 14, step 2).

function [EQ,ERAi,nea] = LSL_equivalence(EQ,ERim1,RLCi,ERAim1,ERAi,NERi,nea,lImg)
    % LSL_EQUIVALENCE build the associative table between er and ea
    % GOAL: to create a Look Up Table to be applied to ERi to create EAi.

    for er = 1:2:NERi % check segments one by one
        % read the boundaries of each segment to obtain de relative labels of every agacent segment in the prev line
        j0 = RLCi(er); 
        j1 = RLCi(er+1);

        er0 = ERim1(j0+1); % label of the first segment
        er1 = ERim1(j1+1); % the label of the last segment

        % check label parity: segments are odd, background is even
        % bitand([1 2 3 4 5],1) == [1 0 1 0 1]
        if bitand(er0,1) == 0 % if er0 is even
            er0 = er0 + 1;
        end
        if bitand(er1,1) == 0 % if er1 is even
            er1 = er1 -1;
        end
        if er1 >= er0 % if there is an adjacency
            ea = ERAim1(er0+1); % absolute label of the first segment 
            a = EQ(ea+1);     % a is the ancestor (smallest label of the equivalence class) 
                for erk = (er0+2):2:er1
                    eak = ERAim1(erk+1);
                    ak = EQ(eak+1);
                    % min extraction and propagation
                    if a < ak
                        EQ(eak+1) = a;
                    else
                        a = ak;
                        EQ(ea+1) = a;
                        ea = eak;
                    end
                end
            ERAi(er+1) = a; % the global min of all ak ancestors 
        else % if there are no adjacent labels make a new label
            nea = nea + 1;
            ERAi(er+1) = nea;
        end
    end
    end

I am having some trouble with indexes, as the pseudo code described in the article has indexes starting with 0 and Matlab works with 1. I have already found some C++ code in this Stack Overflow post Implementing LSL for Connected Component Labeling/Blob Extraction (I applied suggested changes) and also in this git repo https://github.com/prittt/YACCLAB/blob/master/include/labeling_lacassagne_2016_code.inc. I fail to see the differences.

Also, I'm having some trouble understanding what an equivalence class is (which is what goes in matrix EQ). Thanks ahead of time!

Answer 1

I realize this is coming a bit late, but I just put up a piece of code that is similar to what the light speed labeling algorithm does. I'll give a brief description of how I solved the index problem.

The first step of LSL is take each column of pixels and finds the start and stop positions of consecutively labeled pixels. You can do that in Matlab like this:

I = imread('text.png');
[rows,cols] = find(xor(I(2:end,:),I(1:end-1,:)));

What this gives you is the row and column of the start and stop position of each run of pixels in a column, except its non-inclusive indexing. By non-inclusive indexing I mean the indices of pixels runs from I(r(2*n-1),c(2*n-1)) to I(r(2*n)-1,c(2*n)) for each pixel run (n). You should note that the paper operates along rows where the above code operates along columns, but the same principle applies. You should also note that the above code does not cover the circumstance of labeled pixels on the edge of the image.

If you want to see a complete implementation, I posted my code on the Matlab File Exchange. I don't claim that it copies LSL exactly, but it works on many of the same principles.

https://www.mathworks.com/matlabcentral/fileexchange/70323-ftllabel?s_tid=prof_contriblnk