Inside-out optical 2D tracking of tangible objects on a surface oftentimes uses a high-resolution pattern printed on the surface. While De-Bruijn-torus patterns offer maximum information density, their orientation must be known to decode them. Determining the orientation is challenging for patterns with very fine details; traditional algorithms, such as Hough Lines, do not work reliably. We show that a convolutional neural network can reliably determine the orientation of quasi-random bitmaps with 6 × 6 pixels per block within 36 × 36 pixel images taken by a mouse sensor. Mean error rate is below 2°. Furthermore, our model outperformed Hough Lines in a test with arbitrarily rotated low-resolution rectangles. This implies that CNN-based rotation-detection might also be applicable for more general use cases.