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Ultrasonogram is one of the main techniques for the non-invasive observation and the diagnosis of the thyroid gland. And, the thyroid papillary carcinoma (TPC) was usually diagnosed during the regular examination of the thyroid gland. The current diagnosis guideline heavily replies on the experienced clinical endoscopists. This paper comprehensively evaluated four classification algorithms and five image feature extraction algorithms for the TPC diagnosis problem. Our data demonstrated that the Hessian features extracted from the transverse ultrasonograms performed better than those from the longitudinal view. The best model (Acc = 0.9949) was achieved by the seven-layer shallow neural network with the LBP and Hessian features extracted from both the longitudinal and transverse views of the ultrasonograms.