Boundary Attention is a differentiable model that explicitly models boundaries, including contours, corners, and intersections, through a mechanism called boundary attention. Compared to previous classical methods, our model is differentiable, scalable to larger images, and can automatically adapt to the appropriate level of geometric detail for each part of the image. Compared to previous deep methods that find boundaries through end-to-end training, it offers the advantages of sub-pixel accuracy, robustness to noise, and the ability to process any image at its native resolution and aspect ratio.