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In this paper, a new camera calibration algorithm is proposed, which is from the quasi-affine invariance of two parallel circles. Two parallel circles here mean two circles in one plane, or in two parallel planes. They are quite common in our life. Between two parallel circles and their images under a perspective projection, we set up a quasi-affine invariance. Especially, if their images under a perspective projection are separate, we find out an interesting distribution of the images and the virtual intersections of the images, and prove that it is a quasi-affine invariance. The quasi-affine invariance is very useful which is applied to identify the images of circular points. After the images of the circular points are identified, linear equations on the intrinsic parameters are established, from which a camera calibration algorithm is proposed. We perform both simulated and real experiments to verify it. The results validate this method and show its accuracy and robustness. Compared with the methods in the past literatures, the advantages of this calibration method are: it is from parallel circles with minimal number; it is simple by virtue of the proposed quasi-affine invariance; it does not need any matching. Excepting its application on camera calibration, the proposed quasiaffine invariance can also be used to remove the ambiguity of recovering the geometry of single axis motions by conic fitting method in [8] and [9]. In the two literatures, three conics are needed to remove the ambiguity of their method. While, two conics are enough to remove it if the two conics are separate and the quasi-affine invariance proposed by us is taken into account.

The grading evaluation of metacarpophalangeal rheumatoid arthritis (RA) ultrasonic images is a diagnostic challenge that heavily relies on the expertise of trained sonographers. This study presents a grading method for detecting and estimating the geometric and texture features of synovium thickening and bone erosion. Unlike previous studies in this area, this work uses the metrics and texture features of region of interest (ROI). The highlighted feature of metacarpophalangeal bone and the dark feature of the synovial thickening are extracted simultaneously by the segmented method based on the Gaussian scale space. The segmented results are analyzed to extract three quantitative geometric parameters, which are combined with gray-level co-occurrence matrix (GLCM) statistic texture features to describe the ultrasonic image of metacarpophalangeal RA. To obtain the preferable ability of classification, we applied a support vector machine (SVM) and various feature descriptors, including GLCM, local binary patterns (LBP), and GLCM + LBP, to grade the ultrasonic image of metacarpophalangeal RA. Results show that the SVM, based on our feature descriptor, provides the highest accuracy of up to 92.50%, of the four descriptors. The SVM based on GLCM+LBP descriptor shows better accuracy (86.55%) than either SVM + LBP (85.43%) or SVM+GLCM (82.51%) for discriminating among four grade RA ultrasonic images. Overall, this methodology points to a significant grading of metacarpophalangeal RA ultrasound images without medical expert analysis or blood sample analysis, such as detecting C-reactive protein, measuring erythrocyte sedimentation rate, and testing rheumatoid factor. INDEX TERMS Computer aided diagnosis, metacarpophalangeal rheumatoid arthritis, machine learning, Ultrasonic imaging.