## 1 Introduction  
Knee osteoarthritis (OA) is the most frequent form of arthritis among older people. It is the main cause of physical disability and activity limitation among older people. In 2000, 13% of the population in the U.S. were aged 65 and above, and more than half of this population had osteoarthritis in at least one of their joints [1]. It is estimated that the number will increase to at least 20% of the U.S. population, which is ~70 million people, and will have crossed 65-year-olds by 2030, and will be at risk of suffering from OA [1]. Statistical analysis indicated that the U.S. incurred an approximate cost of $336 billion, equivalent to 3% of its gross domestic product (GDP), to treat patients suffering from arthritis in 2004 [2]. The OA disease has been a major cause of increased economic expense burden on the society in the form of early retirement, increased absenteeism from work, as well as the high cost associated with joint replacement [3]. The cause of OA is still unknown, and there is no effective treatment found yet that may slow the progression of OA disease [4]. Measurement of cartilage damage is used as an essential endpoint to assess the structural change of OA progression in clinical studies. The decrease in cartilage is associated with the progression of the OA pathology [5]. According to the previous study [6], changes in the whole knee cartilage layer may demonstrate certain patterns along with the development of the OA. For example, the cartilage regions that bear more weight tend to have more cartilage loss. Very limited research has been done on using machine learning method to model the cartilage changing patterns. In clinical research, magnetic resonance (MR) is considered as a technology that has noninvasive nature which can be used to quantify cartilage. However, it is time-consuming to measure the morphology of cartilages using MR images. The manual segmentation of a 3D knee MR series may take up to 6 h. Moreover, operators need extensive training [7] to accurately measure cartilage. For the past decade, scientists have conducted research to find efficient and reliable methods to measure knee cartilage from the MR images. Some basic strategies include restricting assessments to partial regions of the cartilage or segmenting alternate MR slices [8; 9; 10]. To automate the procedure of cartilage segmentation for MR images, computer-aided algorithms based on B-splines and active contour models have been utilized [8; 9; 11; 12; 13]. However, these approaches were not accurate enough to be used in clinical research, especially in detecting small cartilage changes [10]. There is a great demand to develop a fast quantification method that is sensitive to cartilage change and has good construct validity and reproducibility. In a recent publication, [PERSON] et al. [14] developed the cartilage damage index (CDI), which is an efficient and novel method for quantifying the cartilage volume. Instead of segmenting whole knee cartilage, this approach measures the thickness of the cartilage at certain informative locations (CDI locations) within the reconstructed cartilage layer. The selection of the informative locations is based on the statistical analysis that specific articular cartilage locations may experience more damage. When measuring CDI, a total of 60 locations within the cartilage layer are chosen, including nine locations from each of the four compartments (medial tibia, medial femur, lateral tibia, and lateral femur), and the rest 24 locations from the patella compartment as shown in Figure 1. The CDI method has been tested and applied in several clinical trials supported by federal grants [15]. The statistical analysis from those studies indicated that CDI is correlated with radiographic severity measures of the OA including Kellgren and Lawrence (KL) grade, Joint Space Width (JSW), Joint Space Narrowing (JSN), as well as knee alignment, all with \(p\)-values less than 0.05 [6; 14].