We investigated the ability to use linear perspective to perceive depth from monocular images. Specifically, we focused on the information provided by convergence of parallel lines in an image due to perspective projection. Our stimuli were trapezoid-shaped projected contours, which appear as rectangles slanted in depth. If converging edges of a contour are assumed to be parallel edges of a 3D object, then it is possible in principle to recover its 3D orientation and relative dimensions. This 3D interpretation depends on projected size; hence, if an image contour were scaled, accurate use of perspective predicts changes in perceived slant and shape. We tested this prediction and measured the accuracy and precision with which observers can judge depth from perspective alone. Observers viewed monocular images of slanted rectangles and judged whether the rectangles appeared longer versus wider than a square. The projected contours had varying widths (7, 14, or 21 deg) and side angles (7 or 25 deg), and heights were varied by a staircase procedure to compute a point of subjective equality and 75% threshold for each condition. Observers were able to reliably judge aspect ratios from the monocular images: Weber fractions were 6-9% for the largest rectangles, increasing to as high as 17% for small rectangles with high simulated slant. Overall, the contours judged to be squares were taller than the projections of actual squares, consistent with perceptual underestimation of depth. Judgments were modulated by image size in the direction expected from perspective geometry, but the effect of size was only about 20-30% of what was predicted. We simulated the performance of a Bayesian ideal observer that integrated perspective information with an a priori bias toward compression of depth and which was able to qualitatively model the pattern of results.