MATLAB: How to find a continuous path through the central part of an image

image analysisImage Processing Toolboxpath

I have data from an experimental setup that yields a light "band" in the central part of the image, unless there is a defect (which is what I'm looking for).
This is shown (after contrast adjustment and conversion to B/W) as a dark (0) stripe through a light central region (1) as shown; a model image but the actual scans often look somewhat close to this:
I am trying to find a way to automatically determine if there's a continuous path from the top to the bottom. The answers I've been able to find often involve fitting lines/splines and these paths may not be well suited to that sort of thing since the defects may vary quite a bit and be very tortuous.
Is there any function/method of going through the picture data (typically 256 x 256 pixels) and determining if there is a contiguous series of zeroes going through the "light" (pixel value = 1) region?

Best Answer

Simply label the image. If the white is in two parts, the number of regions will be 2 or more:
[labeledImage, numberOfRegions] = bwlabel(binaryImage);