Calibration, Recognition, and Shape from Silhouettes of Stones

Multi-view shape-from-silhouette systems are increasingly used for analysing stones. This thesis presents methods to estimate stone shape and to recognise individual stones from their silhouettes. Calibration of two image capture setups is investigated. First, a setup consisting of two mirrors and a camera is introduced. Pose and camera internal parameters are inferred from silhouettes alone. Second, the configuration and calibration of a high throughput multi-camera setup is covered. Multiple silhouette sets of a stone are merged into a single set by inferring relative poses between sets. This is achieved by adjusting pose parameters to maximise geometrical consistency specified by the epipolar tangency constraint. Shape properties (such as volume, flatness, and elongation) are inferred more accurately from the merged silhouette sets than from the original silhouette sets. Merging is used to recognise individual stones from pairs of silhouette sets captured on different occasions. Merged sets with sufficient geometrical consistency are classified as matches (produced by the same stone), whereas inconsistent sets are classified as mismatches. Batch matching is determining the one-to-one correspondence between two unordered batches of silhouette sets of the same batch of stones. A probabilistic framework is used to combine recognition by merging (which is slow, but accurate) with the efficiency of computing shape distribution-based dissimilarity values. Two unordered batches of 1200 six-view silhouette sets of uncut gemstones are correctly matched in approximately 68 seconds (using a 3.2GHz Pentium 4 machine). An experiment that compares silhouette-based shape estimates with mechanical sieving demonstrates an application using the developed methods. A batch of 494 garnets is sieved 15 times. After each sieving, silhouette sets are captured for sub-batches in each bin. Batch matching is used to determine the 15 sieve bins per stone. Better estimates of repeatability, and better understanding of the variability of the sieving process is obtained than if only histograms (the natural output of sieving) were considered. Silhouette-based sieve emulation is found to be more repeatable than mechanical sieving.