Texture-like measures for quantifying density of data in binary images
One of the most obvious that comes to mind is MPEG-7's Edge Histogram Descriptor. 

In this, you divide the image into blocks and consider the edge pixels across different angles forming the complete local histogram. This is organized the same way as a Gabor transform features at angular orientation at different angles. This is fairly a very good indicator to classify and search pictures with similarity in their structures and hence edges. 

See this reference 2 which is a great introduction to MPEG 7 color and texture. See Reference 3 for a more detailed coverage for the Local Edge descriptors. 


Thomas Sikora, The MPEG-7 Visual Standard for Content
Description—An Overview IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY, VOL. 11, NO. 6, JUNE 2001 
B. S. Manjunath, Jens-Rainer Ohm, Vinod V. Vasudevan, and
Akio Yamada Color and Texture Descriptors IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY, VOL. 11, NO. 6, JUNE 2001
Dong Kwon Park, Yoon Seok Jeon, Chee Sun Won Efficient Use of Local Edge Histogram Descriptor Proceeding MULTIMEDIA '00 Proceedings of the 2000 ACM workshops on Multimedia Pages 51-54