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Optimal femoral head contour segmentation in CT images using dynamic programming

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Heun's method

In mathematics and computational science, Heun's method may refer to the improved or modified Euler's method (that is, the explicit trapezoidal rule), or a similar two-stage Runge–Kutta method. It is named after Karl Heun and is a numerical procedure for solving ordinary differential equations (ODEs) with a given initial value. Both variants can be seen as extensions of the Euler method into two-stage second-order Runge–Kutta methods.

Jacobi method

In numerical linear algebra, the Jacobi method (a.k.a. the Jacobi iteration method) is an iterative algorithm for determining the solutions of a strictly diagonally dominant system of linear equations. Each diagonal element is solved for, and an approximate value is plugged in. The process is then iterated until it converges. This algorithm is a stripped-down version of the Jacobi transformation method of matrix diagonalization. The method is named after Carl Gustav Jacob Jacobi.

Bone tumor

A bone tumor is an abnormal growth of tissue in bone, traditionally classified as noncancerous (benign) or cancerous (malignant). Cancerous bone tumors usually originate from a cancer in another part of the body such as from lung, breast, thyroid, kidney and prostate. There may be a lump, pain, or neurological signs from pressure. A bone tumor might present with a pathologic fracture. Other symptoms may include fatigue, fever, weight loss, anemia and nausea. Sometimes there are no symptoms and the tumour is found when investigating another problem.

Osteoarthritis

Osteoarthritis (OA) is a type of degenerative joint disease that results from breakdown of joint cartilage and underlying bone which affects 1 in 7 adults in the United States. It is believed to be the fourth leading cause of disability in the world. The most common symptoms are joint pain and stiffness. Usually the symptoms progress slowly over years. Other symptoms may include joint swelling, decreased range of motion, and, when the back is affected, weakness or numbness of the arms and legs.

Degenerative disc disease

Degenerative disc disease (DDD) is a medical condition typically brought on by the normal aging process in which there are anatomic changes and possibly a loss of function of one or more intervertebral discs of the spine. DDD can take place with or without symptoms, but is typically identified once symptoms arise. The root cause is thought to be loss of soluble proteins within the fluid contained in the disc with resultant reduction of the oncotic pressure, which in turn causes loss of fluid volume.

Hip dysplasia

Hip dysplasia is an abnormality of the hip joint where the socket portion does not fully cover the ball portion, resulting in an increased risk for joint dislocation. Hip dysplasia may occur at birth or develop in early life. Regardless, it does not typically produce symptoms in babies less than a year old. Occasionally one leg may be shorter than the other. The left hip is more often affected than the right. Complications without treatment can include arthritis, limping, and low back pain.

Iterated function

In mathematics, an iterated function is a function X → X (that is, a function from some set X to itself) which is obtained by composing another function f : X → X with itself a certain number of times. The process of repeatedly applying the same function is called iteration. In this process, starting from some initial object, the result of applying a given function is fed again in the function as input, and this process is repeated. For example on the image on the right: with the circle‐shaped symbol of function composition.

Active contour model

Active contour model, also called snakes, is a framework in computer vision introduced by Michael Kass, Andrew Witkin, and Demetri Terzopoulos for delineating an object outline from a possibly 2D . The snakes model is popular in computer vision, and snakes are widely used in applications like object tracking, shape recognition, , edge detection and stereo matching. A snake is an energy minimizing, deformable spline influenced by constraint and image forces that pull it towards object contours and internal forces that resist deformation.

Medical imaging

Medical imaging is the technique and process of imaging the interior of a body for clinical analysis and medical intervention, as well as visual representation of the function of some organs or tissues (physiology). Medical imaging seeks to reveal internal structures hidden by the skin and bones, as well as to diagnose and treat disease. Medical imaging also establishes a database of normal anatomy and physiology to make it possible to identify abnormalities.

Graph cuts in computer vision

As applied in the field of computer vision, graph cut optimization can be employed to efficiently solve a wide variety of low-level computer vision problems (early vision), such as , the stereo correspondence problem, , object co-segmentation, and many other computer vision problems that can be formulated in terms of energy minimization. Many of these energy minimization problems can be approximated by solving a maximum flow problem in a graph (and thus, by the max-flow min-cut theorem, define a minimal cut of the graph).