Statistics of Medical Imaging

11

Statistical Imag e Analysis – II

11.1 Introduction

Advanced image analysis techniques, including those applied to medical im-

ages, utilize the spatial relationship of pixels in the images. This relationship

is mainly determined by the properties of the intensities and geometries of

pixels, either local o r global. Among various frameworks of image analysis

techniques such as listed in Section 10.1, descriptors such as “connectivity,”

“continuity,” “smoothness,” a nd “hanging togetherness,” etc., are often em-

ployed to characterize spatial re lationships of pixels.

In the graph approach [1–4], edge contour detection is formulated as a

minimum cos t (the weighted shor test) path problem on a graph. The path cost

function is determined by local image properties: pixel location, intensity, and

gradient. It is applica tion specific. Criteria for the continuity o f arcs and/or

segments of e dges are differ ent and user specified.

In the classical snakes and active contour approaches [4, 6–8], by minimiz-

ing the total energy defined by the models, the edge curve a t the po ints of

maximal magnitude of the gradients are lo cated via the external energy while

the smoothness of the edge curve is kept via the internal energy.

Level set methods [9 , 9, 11, 12]—a variational approach—seek a mini-

mizer of a functional by solving the associated partial differential equations

(PDEs) [13, 14]. These PDEs guide the interface—the evolution of the zero-

level curve—toward the boundary of the optimal par titions.

In the Active Shape model (ASM) and Active Appearance model (AAM)

approaches [14–17, 19, 19–22], the correspo nding points on each sample of a

training set of annotated images are ma rked and aligned. Eigen-analy sis is

then applied to build a statistical shape mo de l. Given enough samples, such

a model is able to synthesize any image of normal a natomy. By adjusting the

parameters that minimize the difference between the synthesized model image

and a target image, all structures, represented and modeled in the image, are

segmented.

In Fuzzy Connected object delineation [21, 22, 25, 26], the strength o f Fuzzy

Connectedness (FC) assigned to a pair of pixels is the strength of the strongest

of all paths between this pair, and the strength of a path is the weakest affinity

between pixels along the path. The degree of affinity between two pixels is

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