Moments of superellipsoids and their application to range image registration.

Cartesian moments are frequently used global geometrical features in computer vision for object pose estimation and recognition. We derive a closed form expression for 3-D Cartesian moment of order p+q+r of a superellipsoid in its canonical coordinate system. We also show how 3-D Cartesian moment of a globally deformed superellipsoid in general position and orientation can be computed as a linear combination of 3-D Cartesian moments of the corresponding nondeformed superellipsoid in canonical coordinate system. Additionally, moments of objects that are compositions of superellipsoids can be computed as simple sums of moments of individual parts. To demonstrate practical application of the derived results we register pairs of range images based on moments of recovered compositions of superellipsoids. We use a standard technique to find centers of gravity and principal axes in pairs of range images while third-order moments are used to resolve the four-way ambiguity. Experimental results show expected improvement of recovered rigid transformation based on moments of recovered superellipsoids as compared to the registration based on moments of raw range image data. Besides object pose estimation the presented results can be directly used for object recognition with moments and/or moment invariants as object features.

Hip stress reduction after Chiari osteotomy.

A mathematical model was developed to study the effect of the Chiari osteotomy on the distribution of contact hip stress over the weight-bearing area. It was shown that Chiari osteotomy can increase the weight-bearing area directly (on the lateral side), owing to the additional area formed by the ala ossis ilii segment, and indirectly (on the medial side), owing to the shift of the stress pole in the medial direction. As a consequence, the contact hip stress is reduced after Chiari osteotomy. The indirect effect is important and often larger than the direct one. Using the proposed mathematical model and standard anteroposterior roentgenographs from archives, the average peak stress on the weight-bearing area, normalised with respect to the body weight (pmax/ W(B)), was determined before and after Chiari osteotomy (8,310m(-2) and 4,480 m(-2), respectively) on a population of 29 dysplastic hips. The difference was statistically significant (p < 0.005). Based on the results presented, it can be concluded that the hip joint contact stress in dysplastic hips considerably decreases after Chiari osteotomy, indicating a favourable biomechanical effect of this operation.

The assessment of contact stress in the hip joint after operative treatment for severe slipped capital femoral epiphysis.

We determined contact stress on the articular surface of the hip joint in a group of patients who underwent operative treatment for severe slipped capital femoral epiphysis. Two different procedures were considered: the modified osteotomy of Dunn-Fish and the osteotomy of Imhäuser. In order to determine the stress distribution, a three-dimensional mathematical model was used taking into account the geometrical parameters of the pelvis and hip, which were measured from standard antero-posterior radiographs. We found that the Dunn-Fish procedure produced lower peak stress than the Imhäuser procedure.

Different operative treatment of slipped capital femoral epiphysis: a comparative study of biomechanical status of the hip.

The biomechanical status of the hips subject to two different operative treatments was studied. The biomechanical status was determined by the peak stress on the weight bearing area using the 3-d mathematical model. It was found that the procedure according to Imhäuser yields considerably and statistically significantly higher peak stress than the procedure according to Dunn-Fish.

Determination of the femoral and pelvic geometrical parameters that are important for the hip joint contact stress: differences between female and male.

The difference between male and female femoral and pelvic geometry was studied by considering some geometrical parameters such as interhip distance, inclination of the crista iliaca, diameter of the femoral head and centre-edge angle of Wiberg. The values of these parameters were determined for 79 healthy female and 21 healthy male subjects. Standard anterior-posterior radiographs were used and processed by the computer-aided system. The results show some important sex differences in femoral and pelvic geometrical parameters which determine the hip joint contact stress.