Jitter noise modeling and its removal using recursive least squares in shape from focus systems.

Three-dimensional shape recovery from the set of 2D images has many applications in computer vision and related fields. Passive techniques of 3D shape recovery utilize a single view point and one of these techniques is Shape from Focus or SFF. In SFF systems, a stack of images is taken with a single camera by manipulating its focus settings. During the image acquisition, the inter-frame distance or the sampling step size is predetermined and assumed constant. However, in a practical situation, this step size cannot remain constant due to mechanical vibrations of the translational stage, causing jitter. This jitter produces Jitter noise in the resulting focus curves. Jitter noise is invisible in every image, because all images in the stack are exposed to the same error in focus; thus, limiting the use of traditional noise removal techniques. This manuscript formulates a model of Jitter noise based on Quadratic function and the Taylor series. The proposed method, then, solves the jittering problem for SFF systems through recursive least squares (RLS) filtering. Different noise levels were considered during experiments performed on both real as well as simulated objects. A new metric measure is also proposed, referred to as depth distortion (DD), which calculates the number of pixels contributing to the RMSE in percentage. The proposed measure is used along with the RMSE and correlation, to compute and test the reconstructed shape quality. The results confirm the effectiveness of the proposed scheme.

Achievement of targeted posterior slope in the medial opening wedge high tibial osteotomy: a mathematical approach.

High tibial osteotomy (HTO) for medial compartment knee osteoarthritis is preferred in the activity patient since it allows patients to return to sports and recreational activities similar to the preoperative level. The purpose of this study was to mathematically formulate medial and anteromedial opening gaps in the medial opening wedge HTO to achieve a targeted tibial posterior slope. The change of posterior slope angle was mathematically derived in terms of the medial and anteromedial opening gaps, and the medial opening angles. The derived equations were validated by comparing them with those directly measured by performing simulated HTOs. In the triangular geometries of osteotomy planes, measured from three-dimensional osteotomy models of 30 knee patients, the mean anteromedial, medial, and lateral included angles were 92.4 degrees, 53.9 degrees, and 33.7 degrees, respectively, and the mean lateral-medial edge length was 53.3 mm. The ratio of the anteromedial opening gap to the posterior opening gap should be "sin(the medial included angle)xcos(the lateral included angle)/sin(the anteromedial included angle)" to maintain an intact posterior tibial slope angle. With the derived equations, surgeons can estimate the opening gaps and opening angles to get a targeted posterior tibial slope with a medial opening angle.

Anatomical evaluation of CT-MRI combined femoral model.

BACKGROUND: Both CT and MRI are complementary to each other in that CT can produce a distinct contour of bones, and MRI can show the shape of both ligaments and bones. It will be ideal to build a CT-MRI combined model to take advantage of complementary information of each modality. This study evaluated the accuracy of the combined femoral model in terms of anatomical inspection. METHODS: Six normal porcine femora (180 +/- 10 days, 3 lefts and 3 rights) with ball markers were scanned by CT and MRI. The 3D/3D registration was performed by two methods, i.e. the landmark-based 3 points-to-3 points and the surface matching using the iterative closest point (ICP) algorithm. The matching accuracy of the combined model was evaluated with statistical global deviation and locally measure anatomical contour-based deviation. Statistical analysis to assess any significant difference between accuracies of those two methods was performed using univariate repeated measures ANOVA with the Turkey post hoc test. RESULTS: This study revealed that the local 2D contour-based measurement of matching deviation was 0.5 +/- 0.3 mm in the femoral condyle, and in the middle femoral shaft. The global 3D contour matching deviation of the landmark-based matching was 1.1 +/- 0.3 mm, but local 2D contour deviation through anatomical inspection was much larger as much as 3.0 +/- 1.8 mm. CONCLUSION: Even with human-factor derived errors accumulated from segmentation of MRI images, and limited image quality, the matching accuracy of CT-&-MRI combined 3D models was 0.5 +/- 0.3 mm in terms of local anatomical inspection.