How to determine the number of white lines in a BW image/vector

Say, I have a vector [ 0 0 0 1 1 1 0 0 0 0 0 1 1 1 1 1 1 0 0 1 1 ]. I want to know how many consecutive '1's in this vector, their lengths, and location.

In this example, we know that there are three consecutive '1's (or white lines). The length is 3 for first one, 5 for second one, and 2 for third one. The location (of the beginning of the white line) is 4 for first one, 12 for the second one, and 20 for the third one.

Eventually I want to have an array to store these info, such as

x = [length, location]

Take the previous example, then x = [3,4; 5,12; 2,20]

How can I realize it with matlab? Prefer a FAST code without running loops! Thank you!!

Answer 1

[Joseph Cheng]

Well you'd start off by detecting the transition from 0 to 1 or 1 to 0. you this can be done by

vect = [0 0 0 1 1 1 0 0 0 0 0 1 1 1 1 1 1 0 0 1 1 ];

det = [vect 0]-circshift([vect 0],[0 1])  

start = find(det==1)
stop = find(det==-1)

outputarray = [(stop-start)' start']

[Ashish Uthama]

If you want this approach, look at DIFF too.

[Yang Zhao]

Thanks Joseph! So smart!

[Yang Zhao]

Hey Ashish. Thanks. It work too! So i just change a piece of Jos's codes to

det = diff([0 vect 0])

[Joseph Cheng]

yup. i used circshift in my test code as some flexibility to shift it in either direction.

Answer 2

[Image Analyst]

I know you already accepted an answer, but if you have the Image Processing Toolbox, you can get all the lengths simply and directly in a single, simple line of code:

measurements = regionprops(logical(vect), 'Area')

Perhaps it might help someone else. Here's a full demo:

vect = [0 0 0 1 1 1 0 0 0 0 0 1 1 1 1 1 1 0 0 1 1 ];
measurements = regionprops(logical(vect), 'Area')

% measurements has the lengths of your 1 regions.
% To show you, you can print them out
for k = 1 : length(measurements);
  fprintf('Region %d has a length of %d elements.\n',k, measurements(k).Area);
end
% If you want, you can get all the lengths into a single array:
allLengths = [measurements.Area]

In the command window you'll see:

measurements = 
3x1 struct array with fields:
    Area
Region 1 has a length of 3 elements.
Region 2 has a length of 6 elements.
Region 3 has a length of 2 elements.
allLengths =
     3     6     2