Knee osteoarthritis is one of the most debilitating aging diseases as it causes loss of cartilage of the knee joint. Knee osteoarthritis affects the quality of life and increases the burden on health care costs. With no disease-modifying osteoarthritis drug currently available there is an immediate need to understand the factors triggering the onset and progression of the disease. Developing robust segmentation techniques and quantitative analysis helps identify potential imaging-based biomarkers that indicate the onset and progression of osteoarthritis. This thesis work developed layered optimal graph image segmentation of multiple objects and surfaces (LOGISMOS) framework based knee MRI segmentation algorithms in 3D and longitudinal 3D (4D). A hierarchical random forest classifier algorithm was developed to improve cartilage costs functions for the LOGISMOS framework. The new cost function design significantly improved the segmentation accuracy over the existing state of the art methods. Disease progression results in more artifacts appearing similar to cartilage in MRI. 4D LOGISMOS segmentation was developed to simultaneously segment multiple time-points of a single patient by incorporating information from earlier time points with a relatively healthier knee in the early stage of the disease. Our experiments showed consistently higher segmentation accuracy across all the time-points over 3D LOGISMOS segmentation of each time-point. Fully automated segmentation algorithms proposed are not 100% accurate especially for patient MRI's having severe osteoarthritis and require interactive correction. An interactive technique called just-enough interaction (JEI) was developed which added a fast correction step to the automated LOGISMOS, speeding up the interactions substantially over the current slice-by-slice manual editing while maintaining high accuracy. JEI editing modifies the graph nodes instead of the boundary surfaces of the bones and cartilages providing globally optimally corrected results. 3D JEI was extended to 4D JEI allowing for simultaneous visualization and interaction of multiple time points of the same patients. Further quantitative analysis tools were developed to study the thickness losses. Nomenclature compliant sub-plate detection algorithm was developed to quantify thickness in the smaller load bearing regions of the knee to help understand the varying rates of thickness losses in the different regions. Regression models were developed to predict the thickness accuracy on a patient MRI at a later follow-up using the available thickness information from the LOGISMOS segmentation of the current set of MRI scans of the patient. Further non-cartilage based imaging biomarker quantification was developed to analyze bone shape changes between progressing and non-progressing osteoarthritic populations. The algorithm quantified statistically significant local shape changes between the two populations. Overall this work improved the state of the art in the segmentation of the bones and cartilage of the femur and tibia. Interactive 3D and 4D JEI were developed allowing for fast corrections of the segmentations and thus significantly improving the accuracy while performing many times faster. Further, the quantitative analysis tools developed robustly analyzed the segmentation providing measurable metrics of osteoarthritis progression.