# How do I access the binary matrix underlying an EdgeDetect output?

Applying EdgeDetect to an image generates a black and white edge-detected image, which I suspect corresponds to an underlying binary matrix. How can I access this underlying data structure, and map between a given matrix position and the corresponding coordinates in the processed image? Ideally, I'd just like a list of, say, the $1$'s or $0$'s in the matrix (whatever corresponds to the white lines in the edge-detected image) and their coordinates.

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With ImageData[]. Like this:
MatrixPlot@ImageData@EdgeDetect@ExampleData[{"TestImage", "Lena"}]