MATLAB: layer detection, vector combination and selection by tortuosity/arclength - image

Question

I have a greyscale image similar to the one below that I have achieved after some post-processing steps (image 0001). I would like a vector corresponding to the bottom of the lower bright strip (as depicted in image 0001b). I can use im2bw with various thresholds to achieve the vectors in image 0002 (the higher the threshold value the higher the tendency for the vector line to blip upwards, the lower the threshold the higher the tendency for the line to blip downwards)..and then I was thinking of going through each vector and measuring arclength over some increment (maybe 100 pixels or so) and choosing that vector with the lowest arclength...and adding that 100 pixel stretch to the final vector, creating a frankenstein-like vector using the straightest segments from each of the thresholded vectors.. I should also mention that when there are multiple straightish/parallel vectors, the top one is the best fit.
First off, is there some better strategy I should be employing here to find that line on image 0001? (this needs to be fast so some long fitting code wouldn't work). If my current Frankenstein's monster solution works, any suggestions as to how to best go about this?
Thanks in advance
image=im2bw(image,0.95); %or 0.85, 0.75, 0.65, 0.55
vec=[];
for v=1:x
for x=1:z
if image(c,v)==1
vec(v)=c;
end
end
end
vec=fastsmooth(vec,60,20,1);

Answer 1

Here is the modified version of what I originally did. It works well on on your images. If you want subpixel resolution, you can implement an active contour model with some fitting function.
files = dir('*.png');
filenames = {files.name};
for ifile=1:length(filenames)
%%
% read image
im0 = double(imread(filenames{ifile}));
%%
% remove background by substracting a convolution with a mask
lobj=100;
convmask = ones(lobj,1)/lobj;
im=im0-conv2(im0,convmask,'same');
im(im<0)=0;
imagesc(im);colormap gray;axis image;
%%
% use canny edge filter, alowing extremely weak edge to exist
bw=edge(im,'canny',[0.01,0.3]);
% use close operation on image to close gaps between lines
% the kernel is a flat rectangular so that it helps to connect horizontal
% gaps
se=strel('rectangle',[10,30]);
bw=imdilate(bw,se);
% thin the lines to be single pixel line
bw=bwmorph(bw,'thin',inf);
% connect H bridge
bw=bwmorph(bw,'bridge');
imagesc(bw);colormap gray;axis image;
%% smooth the image, find the decreasing region, and apply the mask
imtmp = imgaussfilt(im0,3);
imtmp = diff(imtmp);
imtmp = [imtmp(1,:);imtmp];
intensity_decrease_mask = imtmp < 0;
bw = bw & intensity_decrease_mask;
imagesc(bw);colormap gray;axis image;
%%
% find properties of the lines, and find the longest lines
cc=regionprops(bw,'Area','PixelList','Centroid','MajorAxisLength','PixelIdxList');
% now select any lines that is larger than eighth of the image width
cc=cc([cc.MajorAxisLength]>size(bw,2)/8);
%%
% select lines that has average intensity larger than gray level
for i=1:length(cc)
cc(i).meanIntensity = mean(im0(sub2ind(size(im0),cc(i).PixelList(:,2), ...
cc(i).PixelList(:,1) )));
end
cc=cc([cc.meanIntensity]>150);
cnts=reshape([cc.Centroid],2,length(cc))';
%%
% calculate the minimum distance to the bottom right of each edge
for i=1:length(cc)
cc(i).distance2bottomright = sqrt(min((cc(i).PixelList(:,2)-size(im,1)).^2 ...
+ (cc(i).PixelList(:,1)-size(im,2)).^2));
end
% select the bottom edge
[~,minindex]=min([cc.distance2bottomright]);
bottomedge = cc(minindex);
%% clean up the lines a little bit
bwtmp = false(size(bw));
bwtmp(bottomedge.PixelIdxList)=1;
% find the end points to the most left and right
endpoints = bwmorph(bwtmp, 'endpoints');
[endy,endx] = find(endpoints);
[~,minind]=min(endx);
[~,maxind]=max(endx);
pos_most_left = [endx(minind),endy(minind)];
pos_most_right = [endx(maxind),endy(maxind)];
% select the shortest path between left and right
dists = bwdistgeodesic(bwtmp,pos_most_left(1),pos_most_left(2)) + ...
bwdistgeodesic(bwtmp,pos_most_right(1),pos_most_right(2));
dists(isnan(dists))=inf;
bwtmp = imregionalmin(dists);
bottomedge=regionprops(bwtmp,'PixelList');
%% plot the lines
imagesc(im0);colormap gray;axis image;hold on;axis off;
for i=1:length(cc)
plot(cc(i).PixelList(:,1),cc(i).PixelList(:,2),'b','linewidth',2);hold on;
end
plot(bottomedge.PixelList(:,1),bottomedge.PixelList(:,2),'r','linewidth',2);hold on;
print(gcf,num2str(ifile),'-djpeg');
% pause
end

Answer 2

I am not sure this answers your question directly, but I have a lot of experiencing fitting arrays (or matrices in my case) to 3D raster images. We were using relatively low power machines (standard i7 processors 32 gb ram), and had to perform the fitting very quickly (<30 seconds). We also had to validate the fit with a variety of parameters (and again these were 3D rasters fit to a point cloud matrix).
Anyways, the process we used was the fminsearch function internal to Matlab. Documentation can be found here: http://www.mathworks.com/help/optim/functionlist.html
We would start with a plain point-cloud and perform successive manipulations on a per pixel basis to adjust the point-cloud to the raster. Essentially walking through each pixel in the raster to produce the lowest offset between the point cloud and the raster.
I will try to search for some code this afternoon and update my answer, but I might explore this option for your case. I would imagine you could fit a curve to certain pixels (e.g. white pixels) both rapidly and accurately by setting up an optimization function.
I also could help more if I understood your objective better. Are you just trying to fit a line to the high-albedo/white areas?
In the way of example: I can fit a 3D point cloud to the following image by starting with a standard point cloud, the 3D raster, and a minimization function (in this case just RMS error of each individual point in the z axis). Throw an fmin function on there and in a few seconds you get a modified point cloud that fits much better than the standard.