Ebook: Stochastic Modeling for Medical Image Analysis

CRC Press, 2016. — 299.Today’s medical computer-assisted diagnostics (CAD) rely in a great part on fast and noninvasive anatomical (static) and functional (dynamic) imaging that visualizes inner organs of the human body and helps to monitor their state and condition. Earlier imaging modalities produced conventional photography, e.g., an x-ray film; however, at present a majority of CAD-related images are digital. Each static digital image is a collection of numerical values, measured for cells, or sites of a finite two-dimensional (2D) or three-dimensional (3D) lattice. The lattice is typically arithmetic, i.e., its sites are equidistant along the spatial coordinate axes. A 2D image is a slice through the body, i.e., it presents an intersection of an organ or a body part of interest with the lattice. Its 2D cells (typically, squares or rectangles) are traditionally called pixels, standing for picture cells, or elements. A 3D lattice embeds a whole organ or a body part, and its usually cubic 3D cells are called voxels, i.e., volume cells. Dynamic digital images, e.g., digital video streams, add a temporal (time) axis to resulting 3D and 4D spatiotemporal lattices.
The pixel/voxel-wise signal, usually called an intensity or gray level, measures physical properties of a small body area in the corresponding 2D/3D lattice site (cell). In particular, the signal is a quantized absorbed electromagnetic radiation in x-ray and computed tomography (CT) imaging or an acoustic pressure in ultrasound imaging (USI) or a magnitude of an emitted radio-frequency wave encoding spatial hydrogen distribution in magnetic resonance imaging (MRI), exemplified in Figure 0.1. The signals are mostly scalar, although in some cases they can be vectorial too, i.e., if several scalar signals are acquired per lattice site in a multichannel or multiband image, such as, e.g., a dual-echo MRI.
Solutions of almost every CAD task require the use of one or more modalities to collect images of certain medical objects and analyze these images. Individual objects or areas of interest occupy separate continuous or disjoint collections or configurations of the lattice sites and differ in visual appearances and shapes, which should be quantified in terms of signal patterns and the geometric properties of these configurations. Basic image analysis in CAD, surgical simulation, and other real-world medical applications includes linear or nonlinear filtering to suppress noise or the background of individual images, co-registration (alignment) of multiple interrelated images, segmentation (detection and separation) of goal objects or their meaningful parts from their background, and comparisons of the segmented area with the same object in other images acquired for the same subject at different times and/or places or with like objects for other subjects. These operations are instrumental, in particular, for appearance and shape monitoring, object recognition, tracing appearance and shape changes, and shape analysis on anatomical and functional medical images.
Image-guided CAD faces two basic challenging problems: (1) accurate and computationally feasible mathematical modeling of images from different modalities to obtain clinically useful information about the goal objects and (2) accurate and fast inferring of meaningful and clinically valid CAD decisions and/or predictions on the basis of model-guided image analysis. Trade-offs between the high complexity of the medical objects and tight clinical requirements to CAD accuracy and speed call for simple yet sufficiently powerful image/object models and basically unsupervised, i.e., fully automated image processing and analysis.
Stochastic or probabilistic modeling considers static or dynamic images of objects of interest, such as, e.g., lungs, kidneys, or brains in CAD applications, as samples from a certain spatial or spatiotemporal random field that accounts for varying shapes and the visual appearances of goal objects. An image set of combinatorial cardinality is modeled with joint and/or conditional probability distributions of signals, making signal configurations, typical for the goal objects, considerably more probable than all other configurations. Long-standing experience with developing CAD systems has shown that stochastic modeling–based medical image analysis outperforms its heuristic ad hoc alternatives in most practical applications.
This book details original stochastic appearance and shape models with computationally feasible and efficient learning techniques that hold much promise for improving the performance of object detection, segmentation, alignment, and analysis in a number of practically important CAD applications, such as, e.g., early lung cancer, autism, dyslexia, or cardiological diagnostics. The models (Figure 0.2) focus on the first-order marginals (i.e., marginal probability distributions) of pixel/voxel-wise signals and second- or higher-order Markov-Gibbs random fields (MGRF) of these signals and/or labels of regions supporting the goal objects in the lattice. The obtained accurate descriptions of visual appearances and shapes of the goal objects and their background in terms of the signal marginals and spatial conditional dependencies between the signals in the MGRFs help to solve efficiently a number of important and challenging CAD problems, exemplified in part in this book.Medical Imaging Modalities
From Images to Graphical Models
IRF Models: Estimating Marginals
Markov-Gibbs Random Field Models: Estimating Signal Interactions
Applications: Image Alignment
Segmenting Multimodal Images
Segmenting with Deformable Models
Segmenting with Shape and Appearance Priors
Cine Cardiac MRI Analysis
Sizing Cardiac Pathologies