Disclosed are methods and systems for measuring orientation parameters of spherical objects by image processing. Geometric shapes detected in a captured image are measured by generating and scoring models of the geometric shapes, where a high numerical score indicates a good match of the model to the image. The orientation parameters are computed from the geometric parameters measured from the image. A fast, precise, and accurate measurement requires generation and scoring be computationally efficient, meaning that many high-scoring models are generated in a short period of time. Disclosed are embodiments for a multistep measurement process for measuring the orientation parameters of an artificial hip joint from an x-ray image, measuring rotation of a basketball from video frame images, and navigating a spacecraft utilizing sunlight incident on a planetary body.