preferable to estimate the volume of diffusion tensors in its entirety by imposing regularity conditions on the underlying field of tensors. scalar values can be extracted from the diffusion tensor, such as the fractional anisotropy, mean, axial and radial diffusivities, which indirectly measure tissue properties such as the dysmyelination of axonal fibers or the presence of edema. standard scalar image computing methods, such as registration and segmentation, can be applied directly to volumes of such scalar values. however, to fully exploit the information in the diffusion tensor, these methods have been adapted to account for tensor valued volumes when performing registration and segmentation. given the principal direction of diffusion at each location in the volume, it is possible to estimate the global pathways of diffusion through a process known as tractography. however, due to the relatively low resolution of diffusion mri, many of these pathways may cross, kiss or fan at a single location. in this situation, the single principal direction of the diffusion tensor is not an appropriate model for the local diffusion distribution. the most common solution to this problem is to estimate multiple directions of local diffusion using more complex models. these include mixtures of diffusion tensors, q-ball imaging, diffusion spectrum imaging and fiber orientation distribution functions, which typically require hardi acquisition with a large number of gradient directions. as with the diffusion tensor, volumes valued with these complex models require special treatment when applying image computing methods, such as registration and segmentation. functional mri functional magnetic resonance imaging (fmri) is a medical imaging modality that indirectly measures neural activity by observing the local hemodynamics, or blood oxygen level dependent signal (bold). fmri data offers a range of insights, and can be roughly divided into two categories: task related fmri is acquired as the subject is performing a sequence of timed experimental conditions. in block-design experiments, the conditions are present for short periods of time (e.g., 10 seconds) and are alternated with periods of rest. event-related experiments rely on a random sequence of stimuli and use a single time point to denote each condition. the standard approach to analyze task related fmri is the general linear model (glm) resting state fmri is acquired in the absence of any experimental task. typically, the objective is to study the intrinsic network structure of the brain. observations made during rest have also been linked to specific cognitive processes such as encoding or reflection. most studies of resting state fmri focus on low frequency fluctuations of the fmri signal (lf-bold). seminal discoveries include the default network, a comprehensive cortical parcellation, and the linking of network characteristics to behavioral parameters. there is a rich set of methodology used to analyze functional neuroimaging data, and there is often no consensus regarding the best method. instead, researchers approach each problem independently and select a suitable model/algorithm. in this context there is a relatively active exchange among neuroscience, computational biology, statistics, and machine learning communities. prominent approaches include massive univariate approaches that probe individual voxels in the imaging data for a relationship to the experiment condition. the prime approach is the general linear model (glm) multivariate- and classifier based approaches, often referred to as multi voxel pattern analysis or multi-variate pattern analysis probe the data for global and potentially distributed responses to an experimental condition. early approaches used support vector machines (svm) to study responses to visual stimuli. recently, alternative pattern recognition algorithms have been explored, such as random forest based gini contrast or sparse regression and dictionary learning functional connectivity analysis studies the intrinsic network structure of the brain, including the interactions between regions. the majority of such studies focus on resting state data to parcelate the brain or to find correlates to behavioral measures. task specific data can be used to study causal relationships among brain regions (e.g., dynamic causal mapping (dcm) ). when working with large cohorts of subjects, the normalization (registration) of individual subjects into a common reference frame is crucial. a body of work and tools exist to perform normalization based on anatomy (fsl, freesurfer, spm). alignment taking spatial variability across subjects into account is a more recent line of work. examples are the alignment of the cortex based on fmri signal correlation, the alignment based on the global functional connectivity structure both in task-, or resting state data, and the alignment based on stimulus specific activation profiles of individual voxels. software software for medical image computing is a complex combination of systems providing io, visualization and interaction, user interface, data management and computation. typically system architectures are layered to serve algorithm developers, application developers, and users. the bottom layers are often libraries and/or toolkits which provide base computational capabilities; while the top layers are specialized applications which address specific medical problems, diseases, or body systems. additional notes medical image computing is also related to the field of computer vision. an international society, the miccai society represents the field and organizes an annual conference and associated workshops. proceedings for this conference are published by springer in the lecture notes in computer science series. in 2000, n. ayache and j. duncan reviewed the state of the field.