The purpose of this paper is to describe a framework for evaluating image segmentation algorithms. Image segmentation consists of object recognition and delineation. For evaluating segmentation methods, three factors-precision (reliability), accuracy (validity), and efficiency (viability)-need to be considered for both recognition and delineation. To assess precision, we need to choose a figure of merit, repeat segmentation considering all sources of variation, and determine variations in figure of merit via statistical analysis. It is impossible usually to establish true segmentation. Hence, to assess accuracy, we need to choose a surrogate of true segmentation and proceed as for precision. In determining accuracy, it may be important to consider different 'landmark' areas of the structure to be segmented depending on the application. To assess efficiency, both the computational and the user time required for algorithm training and for algorithm execution should be measured and analyzed. Precision, accuracy, and efficiency factors have an influence on one another. It is difficult to improve one factor without affecting others. Segmentation methods must be compared based on all three factors, as illustrated in an example wherein two methods are compared in a particular application domain. The weight given to each factor depends on application. q

Most descriptions of the extensor mechanism of the knee do not take into account its complexity and variability. The quadriceps femoris insertion into the patella is said to be through a common tendon with a threelayered arrangement: rectus femoris (RF) most superficially, vastus medialis (VM) and lateralis (VL) in the intermediate layer, and vastus intermedius (VI) most deeply. We dissected 20 limbs from 17 cadavers to provide a more detailed description of the anterior components of the knee: the tendon, the patellar retinacula, and the patellofemoral ligaments. Only three of the 20 specimens exhibited the typically described quadriceps pattern. The remainder had bilaminar and even more complex trilaminar and tetralaminar fiber arrangements. We found an oblique head of the vastus lateralis (VLO), separated from the longitudinal head by a layer of fat or fascia, in 60% of the specimens. However, we found no distinct oblique head of the vastus medialis (VMO) in any specimen. The medial patellofemoral ligament (MPFL) was more common than the lateral (LPFL), supporting its suggested role as the principal passive medial stabilizer of the patella. Because the quadriceps muscle group plays a direct role in patellofemoral joint function, investigation into the clinical applications of its highly variable anatomy may be worthwhile with respect to joint dysfunction and failures of TKAs.

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Common image-based diagnostic techniques used to detect ankle ligament injuries or the effects of those injuries (e.g., mechanical instability) include magnetic resonance imaging (MRI) and stress radiography. Each of these techniques has limitations. The interpretation of the results obtained through stress radiography, a two-dimensional technique, is highly controversial. MRI can facilitate visualization of soft tissue, but three-dimensional visualization of the full length of the ligaments or detecting partial ligament damage is difficult. This work is part of a long-term study aimed at improving the diagnostic ability of MRI by utilizing it not only to visualize the ligaments but also to detect the mechanical instability produced at the ankle and subtalar joints due to ligament damage. The goal of the present study was to evaluate the ability of a previously developed technique called 3D stress MRI (sMRI) to detect in vitro the effect of damage to the lateral collateral ligaments and the stabilizing effect produced by two common surgical reconstruction techniques. MRI data were collected from eight cadaver limbs in a MR compatible ankle-loading device in neutral, inversion, and anterior drawer. Each specimen was tested intact, after cutting the anterior talo-fibular ligament followed by the calcaneo-fibular ligament and after applying two reconstructions. Ligament injuries produced significant changes in the response of the ankle and subtalar joints to load as detected by the 3D stress MRI technique. Both surgical procedures restored mechanical stability to the joints but they differed in the amount and type of stabilization achieved. We concluded that 3D sMRI can extend the diagnostic power of MRI from the current practice of slice-by-slice visualization to the assessment of mechanical function, the compromise in this function due to injury, and the effects of surgery.

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Objective. To compare in vivo the 3-dimensional (3-D) geometric architecture of the subtalar and midtarsal joints in normal and rheumatoid arthritic (RA) feet, using magnetic resonance imaging (MRI) analysis.Methods. MRI was performed on 23 patients with RA, all of whom had disease activity in the subtalar and/or midtarsal joints. Image processing techniques were used to create 3-D reconstructions of the calcaneus (C), cuboid (c), navicular (N), and talus (T) bones. Twenty-four standard architectural parameters were measured from the reconstructions and were compared with data from 10 normal subjects. These parameters defined both 3-D distance and angular relationships among the 4 bones studied. Pattern classification techniques were used to establish a geometric architecture foot profile for the RA patients. The degree of individual patient fit to the new RA foot profile and to profiles for normal, pes planus, and pes cavus foot types was derived. Logistic regression was used to examine the relationship of foot architecture to inflammatory disease characteristics and physical examination variables.Results. Subtalar or midtarsal pain was reported by all 23 patients, and 22 of the 23 patients presented with >1 clinical feature of pes planovalgus deformity. In 21 patients, ultrasonography revealed synovitis at >1 tarsal joint or surrounding tendon. In the RA group, the normalized distances between the geometric centroids were significantly closer for bone pairs Cc and cT and significantly distracted for bone pair CN compared with the distances in normal subjects. In RA patients (versus normal subjects), the angles subtended at the bone centroids were significantly decreased in 3 bone groups (CNc, TCN, and TNc) and significantly increased in 3 bone groups (CcN, CcT, NTc). The angles formed between the major principal axes of bone pairs CT and cT were significantly increased in RA patients compared with those in normal subjects. Pattern classification defined 11 RA feet as having normal structure and 12 as having abnormal structure. However, the abnormal feet did not fit consistently with structures defined for RA, pes planus, or pes cavus foot types. Logistic regression demonstrated that subtalar joint synovitis was the only predictive factor for abnormal subtalar and midtarsal architecture (odds ratio 19.2, 95% confidence interval 1.77-200.0).Conclusion. This unique 3-D MRI-based technique successfully quantified the effects of RA on the geometric architecture of the foot and the patientspecific nature of these changes. This technique can be used to provide logical therapy for correction.

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A new method of measuring the kinematic parameters of joints has been developed. This article describes the procedure, using tarsal joints as examples. The method uses the technique of computerized three-dimensional reconstruction from magnetic resonance images, taken at regular intervals throughout a foot's range of motion. From these reconstructions, various kinematic information, such as orientation of instantaneous axes, amounts of rotation, amounts and direction of translation, and bony contact areas, is derived. The method is noninvasive and can be applied to individual subjects or patients.