In low-resource areas, the most common method of tuberculosis (TB) diagnosis is visual identification of rod-shaped TB bacilli in microscopic images of sputum smears. We present an algorithm for automated TB detection using images from digital microscopes such as CellScope, a novel, portable device capable of brightfield and fluorescence microscopy. Automated processing on such platforms could save lives by bringing healthcare to rural areas with limited access to laboratory-based diagnostics. Our algorithm applies morphological operations and template matching with a Gaussian kernel to identify candidate TB-objects. We characterize these objects using Hu moments, geometric and photometric features, and histograms of oriented gradients and then perform support vector machine classification. We test our algorithm on a large set of CellScope images (594 images corresponding to 290 patients) from sputum smears collected at clinics in Uganda. Our object-level classification performance is highly accurate, with average precision of 89.2% +/- 2.1%. For slide-level classification, our algorithm performs at the level of human readers, demonstrating the potential for making a significant impact on global healthcare.