If you already have the green path and just want to divide it in segments, I'd transform the coordinates of the green paths into a logical matrix. Then you can easily find the borders of the segment and display it as you want.

matrixSize = 600;

%Your green path 2 column vector
xPositions = greenPath(:,1);
yPositions = greenPath(:,2);

%Transform to logical matrix
greenPathMat = false(matrixSize);
idx = sub2ind([matrixSize, matrixSize], yPositions, xPositions);
greenPathMat(idx) = true;

%Get border in x and y direction
xBorders = diff(m,1,2);
yBorders = diff(m,1,1);

%Get Start and End
xStart = find(any(xBorders==1)) + 1;
xEnd = find(any(xBorders==-1));

yStart = find(any(yBorders==1,2)) + 1;
yEnd = find(any(yBorders==-1,2));

%Check if there are any values at matrix borders to add them to start/end
if any(m(:,1));    xStart = [1 xStart]; end

if any(m(:,end));    xEnd = [xEnd, matrixSize];  end

if any(m(1,:));    yStart = [1; yStart];    end

if any(m(end,:));    yEnd = [yEnd; matrixSize];  end

%Calc number of segments
nbSegments = length(xStart) * 2;

if length(xStart) == length(xEnd)
    nbSegments = nbSegments - 1;
end

%Display path in black and white
imagesc(greenPathMat)
set(gca,"YDir","normal")
hold on
colormap gray

for ii = 1:floor(nbSegments/2)
    %Vertical segments
    plot(polyshape([xStart(ii) xStart(ii) xEnd(ii) xEnd(ii)],...
        [yStart(ii) yEnd(ii) yEnd(ii) yStart(ii)]));

    %Horizontal segments
    plot(polyshape([xStart(ii) xStart(ii) xEnd(ii+1) xEnd(ii+1)],...
        [yStart(ii+1) yEnd(ii) yEnd(ii) yStart(ii+1)]));
end

%If last segment is vertical
if length(xStart) == length(xEnd)
    plot(polyshape([xStart(ii+1) xStart(ii+1) xEnd(ii+1) xEnd(ii+1)],...
        [yStart(ii+1) yEnd(ii+1) yEnd(ii+1) yStart(ii+1)]));
end

If you plot them one by one it looks like this. Is this what you want?