Perhaps you could try the following to get a rough estimate for total length without skeletonizing the image:
(1) enhance edge/ridge information such as median filtering to reduce level of noise specks in image (NB this should eliminate the small specks but not large dots shown)
(2) apply thresholding to binarise the image (for automatic global threshold e.g. otsu method)
(3) apply dilation and erosion to reduce branches to single pixel thickness
(4) count the number of pixels above threshold in processed binary image
(5) to estimate length, multiply total count of pixels by spatial dimension of each pixel (assuming dx=dy)
By first applying this approach to a random sample of subimages and comparing the estimates to hand tracing you can then check whether this rough approach will accurate enough for your needs.