Objective The aim of the present study was to compare the reliability and agreement between a computer tomography-based method (CT) and digitalised 2D radiographs (XR) when measuring change in dorsal angulation over time in distal radius fractures. Materials and methods Radiographs from 33 distal radius fractures treated with external fixation were retrospectively analysed. All fractures had been examined using both XR and CT at six times over 6 months postoperatively. The changes in dorsal angulation between the first reference images and the following examinations in every patient were calculated from 133 follow-up measurements by two assessors and repeated at two different time points. The measurements were analysed using Bland-Altman plots, comparing intra- and inter-observer agreement within and between XR and CT. Results The mean differences in intra- and inter-observer measurements for XR, CT, and between XR and CT were close to zero, implying equal validity. The average intra- and inter-observer limits of agreement for XR, CT, and between XR and CT were +/- 4.4 degrees, +/- 1.9 degrees and +/- 6.8 degrees respectively. Conclusions For scientific purpose, the reliability of XR seems unacceptably low when measuring changes in dorsal angulation in distal radius fractures, whereas the reliability for the semi-automatic CT-based method was higher and is therefore preferable when a more precise method is requested.

Purpose

To test the hypothesis that a whole-body fat–water MRI (FWMRI) protocol acquired at 3 Tesla combined with semi-automated image analysis techniques enables precise volume and mass quantification of adipose, lean, and bone tissue depots that agree with static scale mass and scale mass changes in the context of a longitudinal study of large-breed dogs placed on an obesogenic high-fat, high-fructose diet.

Materials and Methods

Six healthy adult male dogs were scanned twice, at weeks 0 (baseline) and 4, of the dietary regiment. FWMRI-derived volumes of adipose tissue (total, visceral, and subcutaneous), lean tissue, and cortical bone were quantified using a semi-automated approach. Volumes were converted to masses using published tissue densities.

Results

FWMRI-derived total mass corresponds with scale mass with a concordance correlation coefficient of 0.931 (95% confidence interval = [0.813, 0.975]), and slope and intercept values of 1.12 and −2.23 kg, respectively. Visceral, subcutaneous and total adipose tissue masses increased significantly from weeks 0 to 4, while neither cortical bone nor lean tissue masses changed significantly. This is evidenced by a mean percent change of 70.2% for visceral, 67.0% for subcutaneous, and 67.1% for total adipose tissue.

Conclusion

FWMRI can precisely quantify and map body composition with respect to adipose, lean, and bone tissue depots. The described approach provides a valuable tool to examine the role of distinct tissue depots in an established animal model of human metabolic disease.

Intentional cranial deformations (ICD) have been observed worldwide but are especially prevalent in preColombian cultures. The purpose of this study was to assess the consequences of ICD on three cranial cavities (intracranial cavity, orbits, and maxillary sinuses) and on cranial vault thickness, in order to screen for morphological changes due to the external constraints exerted by the deformation device. We acquired CT-scans for 39 deformed and 19 control skulls. We studied the thickness of the skull vault using qualitative and quantitative methods. We computed the volumes of the orbits, of the maxillary sinuses, and of the intracranial cavity using haptic-aided semi-automatic segmentation. We finally defined 3D distances and angles within orbits and maxillary sinuses based on 27 anatomical landmarks and measured these features on the 58 skulls. Our results show specific bone thickness patterns in some types of ICD, with localized thinning in regions subjected to increased pressure and thickening in other regions. Our findings confirm that volumes of the cranial cavities are not affected by ICDs but that the shapes of the orbits and of the maxillary sinuses are modified in circumferential deformations. We conclude that ICDs can modify the shape of the cranial cavities and the thickness of their walls but conserve their volumes. These results provide new insights into the morphological effects associated with ICDs and call for similar investigations in subjects with deformational plagiocephalies and craniosynostoses.

Prostate MRI image segmentation has been an area of intense research due to the increased use of MRI as a modality for the clinical workup of prostate cancer. Segmentation is useful for various tasks, e.g. to accurately localize prostate boundaries for radiotherapy or to initialize multi-modal registration algorithms. In the past, it has been difficult for research groups to evaluate prostate segmentation algorithms on multi-center, multi-vendor and multi-protocol data. Especially because we are dealing with MR images, image appearance, resolution and the presence of artifacts are affected by differences in scanners and/or protocols, which in turn can have a large influence on algorithm accuracy. The Prostate MR Image Segmentation (PROMISE12) challenge was setup to allow a fair and meaningful comparison of segmentation methods on the basis of performance and robustness. In this work we will discuss the initial results of the online PROMISE12 challenge, and the results obtained in the live challenge workshop hosted by the MICCAI2012 conference. In the challenge, 100 prostate MR cases from 4 different centers were included, with differences in scanner manufacturer, field strength and protocol. A total of 11 teams from academic research groups and industry participated. Algorithms showed a wide variety in methods and implementation, including active appearance models, atlas registration and level sets. Evaluation was performed using boundary and volume based metrics which were combined into a single score relating the metrics to human expert performance. The winners of the challenge where the algorithms by teams Imorphics and ScrAutoProstate, with scores of 85.72 and 84.29 overall. Both algorithms where significantly better than all other algorithms in the challenge (p < 0.05) and had an efficient implementation with a run time of 8 min and 3 s per case respectively. Overall, active appearance model based approaches seemed to outperform other approaches like multi-atlas registration, both on accuracy and computation time. Although average algorithm performance was good to excellent and the Imorphics algorithm outperformed the second observer on average, we showed that algorithm combination might lead to further improvement, indicating that optimal performance for prostate segmentation is not yet obtained. All results are available online at http://promise12.grand-challenge.org/. (C) 2013 Elsevier B.V. All rights reserved.

The subject of digital image analysis deals with extracting relevant information from image data, stored in digital form in a computer. A fundamental problem in image analysis is image segmentation, i.e., the identification and separation of relevant objects and structures in an image. Accurate segmentation of objects of interest is often required before further processing and analysis can be performed.

Despite years of active research, fully automatic segmentation of arbitrary images remains an unsolved problem. Interactive, or semi-automatic, segmentation methods use human expert knowledge as additional input, thereby making the segmentation problem more tractable. The goal of interactive segmentation methods is to minimize the required user interaction time, while maintaining tight user control to guarantee the correctness of the results. Methods for interactive segmentation typically operate under one of two paradigms for user guidance: (1) Specification of pieces of the boundary of the desired object(s). (2) Specification of correct segmentation labels for a small subset of the image elements. These types of user input are referred to as boundary constraints and regional constraints, respectively.

This thesis concerns the development of methods for interactive segmentation, using a graph-theoretic approach. We view an image as an edge weighted graph, whose vertex set is the set of image elements, and whose edges are given by an adjacency relation among the image elements. Due to its discrete nature and mathematical simplicity, this graph based image representation lends itself well to the development of efficient, and provably correct, methods.

The contributions in this thesis may be summarized as follows:

• Existing graph-based methods for interactive segmentation are modified to improve their performance on images with noisy or missing data, while maintaining a low computational cost.
• Fuzzy techniques are utilized to obtain segmentations from which feature measurements can be made with increased precision.
• A new paradigm for user guidance, that unifies and generalizes regional and boundary constraints, is proposed.

The practical utility of the proposed methods is illustrated with examples from the medical field.

The Image Foresting Transform (IFT) is a framework forimage partitioning, commonly used for interactive segmentation. Givenan image where a subset of the image elements (seed-points) have beenassigned user-defined labels, the IFT completes the labeling by computingminimal cost paths from all image elements to the seed-points. Eachimage element is then given the same label as the closest seed-point. Inits original form, the IFT produces crisp segmentations, i.e., each imageelement is assigned the label of exactly one seed-point. Here, we proposea modified version of the IFT that computes region boundaries withsub-pixel precision by allowing mixed labels at region boundaries. Wedemonstrate that the proposed sub-pixel IFT allows properties of thesegmented object to be measured with higher precision.

Many image segmentation methods utilize graph structures for representing images, where the flexibility and generality of the abstract structure is beneficial. By using a fuzzy object representation, i.e., allowing partial belongingness of elements to image objects, the unavoidable loss of information when representing continuous structures by finite sets is significantly reduced,enabling feature estimates with sub-pixel precision.This work presents a framework for object representation based on fuzzysegmented graphs. Interpreting the edges as one-dimensional paths betweenthe vertices of a graph, we extend the notion of a graph cut to that of a located cut, i.e., a cut with sub-edge precision. We describe a method for computing a located cut from a fuzzy segmentation of graph vertices. Further,the notion of vertex coverage segmentation is proposed as a graph theoretic equivalent to pixel coverage segmentations and a method for computing such a segmentation from a located cut is given. Utilizing the proposed framework,we demonstrate improved precision of area measurements of synthetic two-dimensional objects. We emphasize that although the experiments presented here are performed on two-dimensional images, the proposed framework is defined for general graphs and thus applicable to images of any dimension.

The stochastic watershed is a method for unsupervised image segmentation proposed by Angulo and Jeulin (2007). The method first computes a probability density function (PDF), assigning to each piece of contour in the image the probability to appear as a segmentation boundary in seeded watershed segmentation with randomly selected seeds. Contours that appear with high probability are assumed to be more important. This PDF is then post-processed to obtain a final segmentation. The main computational hurdle with the stochastic watershed method is the calculation of the PDF. In the original publication by Angulo and Jeulin, the PDF was estimated by Monte Carlo simulation, i.e., repeatedly selecting random markers and performing seeded watershed segmentation. Meyer and Stawiaski (2010) showed that the PDF can be calculated exactly, without performing any Monte Carlo simulations, but do not provide any implementation details. In a naive implementation, the computational cost of their method is too high to make it useful in practice. Here, we extend the work of Meyer and Stawiaski by presenting an efficient (quasi-linear) algorithm for exact computation of the PDF. We demonstrate that in practice, the proposed method is faster than any previously reported method by more than two orders of magnitude. The algorithm is formulated for general undirected graphs, and thus trivially generalizes to images with any number of dimensions.

Seeded segmentation with minimum spanning forests, also known as segmentation by watershed cuts, is a powerful method for supervised image segmentation. Given that correct segmentation labels are provided for a small set of image elements, called seeds, the watershed cut method completes the labeling for all image elements so that the boundaries between different labels are optimally aligned with salient edges in the image. Here, a randomized version of watershed segmentation, the targeted stochastic watershed, is proposed for performing multi-label targeted image segmentation with stochastic seed input. The input to the algorithm is a set of probability density functions (PDFs), one for each segmentation label, defined over the pixels of the image. For each pixel, we calculate the probability that the pixel is assigned a given segmentation label in seeded watershed segmentation with seeds drawn from the input PDFs. We propose an efficient algorithm (quasi-linear with respect to the number of image elements) for calculating the desired probabilities exactly.

We present SmartPaint, a general-purpose method and software for interactive segmentation of medical volume images. SmartPaint uses a novel paint-brush interaction paradigm, where the user segments objects in the image by 'sweeping' over them with the mouse cursor. The key feature of SmartPaint is that the painting tools adapt to the image content, selectively sticking to objects of interest while avoiding other structures. This behaviour is achieved by modulating the effect of the tools by both the Euclidean distance and the range distance (difference in image intensity values) from the mouse cursor. We evaluate SmartPaint on three publicly available medical image datasets, covering different image modalities and segmentation targets. The results show that, with a limited user effort, SmartPaint can produce segmentations whose accuracy is comparable to both the state-of-the-art automatic segmentation methods and manual delineations produced by expert users. The SmartPaint software is freely available, and can be downloaded from the authors' web page (http://www.cb.uu.se/similar to filip/SmartPaint/).

The Image Foresting Transform (IFT) is a framework for efficient image partitioning, used in interactive segmentation. We propose a modified version of the IFT, and demonstratethat the modified algorithm is more robust to noise while maintaining computational complexity. We also show an application of the method for interactive segmentation ofback muscles in magnetic resonance images, where seedpoints representing object and background are placed repeatedly until a desired segmentation result is obtained.

The stochastic watershed is a method for identifying salient contours in an image, with applications to image segmentation. The method computes a probability density function (PDF), assigning to each piece of contour in the image the probability to appear as a segmentation boundary in seeded watershed segmentation with randomly selected seedpoints. Contours that appear with high probability are assumed to be more important. This paper concerns an efficient method for computing the stochastic watershed PDF exactly, without performing any actual seeded watershed computations. A method for exact evaluation of stochastic watersheds was proposed by Meyer and Stawiaski (2010). Their method does not operate directly on the image, but on a compact tree representation where each edge in the tree corresponds to a watershed partition of the image elements. The output of the exact evaluation algorithm is thus a PDF defined over the edges of the tree. While the compact tree representation is useful in its own right, it is in many cases desirable to convert the results from this abstract representation back to the image, e. g, for further processing. Here, we present an efficient linear time algorithm for performing this conversion.

Deformable image registration, the task of nding a spatial transformation that aligns two or more images with each other, is an important task in medical image analysis. To a large extent, research on image registration has been focused on automatic methods. This is in contrast to, e.g., image segmentation, where interactive semi-automatic methods are common. Here, we propose a method for interactive editing of a deformation eld aligning two volume images. The method has been implemented in a software that allows the user to click and drag points in the deformed image to a new location, while smoothly deforming surrounding points. The method is fast enough to allow real-time display of the deformed volume image during user interaction, on standard hardware. The resulting tool is useful for initializing automatic methods, and to correct errors in automatically generated registrations.

This paper describes a general method for interactive segmentation, Smart Paint. The user interaction is inspired by the way an airbrush is used, objects are segmented by "sweeping" with the mouse cursor in the image. The user adds or removes details in 3D by the proposed segmentation tool and the user interface shows the segmentation result in 2D slices through the object. We use the novel method for prostate segmentation in transversal T2-weighted MR images from multiple centers and vendors and with differences in scanning protocol.

The method was evaluated on the training set obtained from http://promise12.grand-challenge.org. In the first round, all 50 volumes were segmented and the mean of Dice's coefficient was 0.82 with standard deviation 0.09. In a second round, the first 30 volumes were re-segmented by the same user and the result was slightly improved -- Dice's coefficient 0.86 $\pm$ 0.05 was obtained. For the training data, the mean time to segment a volume was 3 minutes and 30 seconds.

The proposed method is a generic tool for interactive image segmentation and this paper illustrates that it is well-suited for prostate segmentation.

Seeded segmentation methods attempt to solve the segmentation problem in the presence of prior knowledge in the form of a partial segmentation, where a small subset of the image elements (seed-points) have been assigned correct segmentation labels. Common for most of the leading methods in this area is that they seek to find a segmentation where the boundaries of the segmented regions coincide with sharp edges in the image. Here, we instead propose a method for seeded segmentation that seeks to divide the image into areas of homogeneous pixel values. The method is based on the computation of minimal cost paths in a discrete representation of the image, using a novel path-cost function. The utility of the proposed method is demonstrated in a case study on segmentation of white matter hyperintensitities in MR images of the human brain.

Designing interactive segmentation methods for digital volume images is difficult, mainly because efficient 3D interaction is much

harder to achieve than interaction with 2D images. To overcome this issue, we use a system that combines stereo graphics and haptics to facilitate efficient 3D interaction. We propose a new method, based on the 2D live-wire method, for segmenting volume images. Our method consists of two parts: an interface for drawing 3D live-wire curves onto the boundary of an object in a volume image, and an algorithm for connecting two such curves to create a discrete surface.

In this paper, we present a method for segmenting phase contrast volume images of fibrous materials into fibre and background. The method is based on graph cut segmentation, and is tested on high resolution X-ray microtomography volume images of wood fibres in paper an composites. The new method produces better results than a standard method based on edge-preserving smoothing and hysteresis thresholding. The most important improvement is that the proposed method handles thick and collapsed fibres more accurately than previous methods.

Intracranial volume (ICV) normalization of regional brain volumes (v) is common practice in volumetric studies of the aging brain. Multiple normalization methods exist and this study aimed to investigate when each method is appropriate to use in gender dimorphism studies and how differences in v are affected by the choice of method. A new method based on weighted ICV matching is also presented. Theoretical reasoning and simulated experiments were followed by an evaluation using real data comprising 400 subjects, all 75 years old, whose ICV was segmented with a gold standard method. The presented method allows good visualization of volume relation between gender groups. A different gender dimorphism in volume was found depending on the normalization method used for both simulated and real data. Method performance was also seen to depend on the slope (B) and intercept (m) from the linear relation between v and ICV (v=B·ICV+m) as well as gender distribution in the cohort. A suggested work-flow for selecting ICV normalization method when investigating gender related differences in regional brain volume is presented.

In brain volumetric studies, intracranial volume (ICV) is often used as an estimate of pre-morbid brain size as well as to compensate for inter-subject variations in head size. However, if the estimated ICV is biased by for example gender or atrophy, it could introduce errors in study results. To evaluate how two commonly used methods for ICV estimation perform, computer assisted reference segmentations were created and evaluated. Segmentations were created for 399 MRI volumes from 75-year-old subjects, with 53 of these subjects having an additional scan and segmentation created at age 80. ICV estimates from Statistical Parametric Mapping (SPM, version 8) and Freesurfer (FS, version 5.1.0) were compared to the reference segmentations, and bias related to skull size (approximated with the segmentation measure), gender or atrophy were tested for. The possible ICV related effect on associations between normalized hippocampal volume and factors gender, education and cognition was evaluated by normalizing hippocampal volume with different ICV measures. Excellent agreement was seen for inter- (r=0.999) and intra- (r=0.999) operator reference segmentations. Both SPM and FS overestimated ICV. SPM showed bias associated with gender and atrophy while FS showed bias dependent on skull size. All methods showed good correlation between time points in the longitudinal data (reference: 0.998, SPM: 0.962, FS: 0.995). Hippocampal volume showed different associations with cognition and gender depending on which ICV measure was used for hippocampal volume normalization. These results show that the choice of method used for ICV estimation can bias results in studies including brain volume measurements.

User-friendly virtual surgery planning(VSP) systems for reconstructive surgery, such as cranio-maxillofacial (CMF) surgery, that can be used by the surgeons themselves without help of a technician have the potential to shorten the pre-operative planning from days to hours. An important part of such systems is the design of surgical guides and plates for osteosynthesis. We describe a method for generating surgical guide and plate models from computed tomography (CT) images, using signed distance fields and constructive solidgeometry (CSG). We implement the method as an extension to our Haptics-Assisted Surgery Plan-ning (HASP) system that enables a user to quickly design guide and plate models with stereo graphics and haptic feedback. We find that surgical guide and plate models can be efficiently generated from segmented CT images with our method. We also find that an anti-aliased distance transform can improve the accuracy and precision of the modelingin this application.

The wrist is the most common location for long-bone fractures in humans. To evaluate the healing process of such fractures, it is of interest to measure the fracture displacement, particularly the angle between the joint line and the long axis of the fractured long bone. We propose to measure this angle in 3D computed tomography (CT) images of fractured wrists. As a first step towards this goal, we here present a fast and precise semi-automatic method for determining the long axis of the radius bone in CT images. To facilitate user interaction in 3D, we utilize stereo graphics, head tracking, 3D input, and haptic feedback.

The clinically established method to assess the displacement of a distal radius fracture is to manually measure two reference angles,the dorsal angle and the radial angle, in consecutive 2D X-ray images of the wrist. This approach has the disadvantage of being sensitive to operator errors since the measurements are performed on 2D projections of a 3D structure. In this paper, we present a semi-automatic system for measuring relative changes in the dorsal angle in 3D computed tomography (CT) images of fractured wrists. We evaluate the proposed 3D measurement method on 28 post-operative CT images of fractured wrists and compare it with the radiographic 2D measurement method used in clinical practice. The results show that our proposed 3D measurement method has a high intra- and inter-operator precision and is more precise and robust than the conventional 2D measurement method.

We present an efficient interactive tool for separating collectively segmented bones and bone fragments in 3D computed tomography (CT) images. The tool, which is primarily intended for virtual cranio-maxillofacial (CMF) surgery planning, combines direct volume rendering with an interactive 3D texture painting interface to enable quick identification and marking of individual bone structures. The user can paint markers (seeds) directly on the rendered bone surfaces as well as on individual CT slices. Separation of the marked bones is then achieved through the random walks segmentation algorithm, which is applied on a graph constructed from the collective bone segmentation. The segmentation runs on the GPU and can achieve close to real-time update rates for volumes as large as 512^3. Segmentation editing can be performed both in the random walks segmentation stage and in a separate post-processing stage using a local 3D editing tool. In a preliminary evaluation of the tool, we demonstrate that segmentation results comparable with manual segmentations can be obtained within a few minutes.

In this paper, we present an efficient interactive tool for segmenting and measuring the volume of the bony orbit (eye-socket) in computed tomography (CT) images. The tool implements a 3D painting interface that allows the user to quickly segment or "paint" the fat and soft-tissue content of the orbit by sweeping a volumetric brush over the image. The brush modifies and updates the segmentation result in real-time and takes distance and gradient information into account to fill out and find the exact boundaries of the orbit. A smooth and consistent delineation of the anterior boundary is obtained by fitting a thin-plate spline to user-selected landmarks. We evaluate the tool on 10 CT images of intact and fractured orbits and show that it achieves high intra- and inter-operator precision (mean spatial overlap 95%, less than 1 ml volume variability) and produces segmentation results that are similar to manually corrected reference segmentations, but only requires a few minutes of interaction time.

BACKGROUND:

Prenatal exposure to bisphenol A (BPA) has been shown to induce obesity in rodents. To evaluate if exposure also later in life could induce obesity or liver damage we investigated these hypothesises in an experimental rat model.

METHODS:

From five to fifteen weeks of age, female Fischer 344 rats were exposed to BPA via drinking water (0.025, 0.25 or 2.5mgBPA/L) containing 5% fructose. Two control groups were given either water or 5% fructose solution. Individual weight of the rats was determined once a week. At termination magnetic resonance imaging was used to assess adipose tissue amount and distribution, and liver fat content. After sacrifice the left perirenal fat pad and the liver were dissected and weighed. Apolipoprotein A-I in plasma was analyzed by western blot.

RESULTS:

No significant effects on body weight or the weight of the dissected fad pad were seen in rats exposed to BPA, and MRI showed no differences in total or visceral adipose tissue volumes between the groups. However, MRI showed that liver fat content was significantly higher in BPA-exposed rats than in fructose controls (p=0.04). BPA exposure also increased the apolipoprotein A-I levels in plasma (p<0.0001).

CONCLUSION:

We found no evidence that BPA exposure affects fat mass in juvenile fructose-fed rats. However, the finding that BPA in combination with fructose induced fat infiltration in the liver at dosages close to the current tolerable daily intake (TDI) might be of concern given the widespread use of this compound in our environment.

Objective: The aim of this study was to setup a rodent model for modest weight gain and an MRI-based quantification of body composition on a clinical 1.5 T MRI system for studies of obesity and environmental factors and their possible association. Design and Methods: Twenty-four 4-week-old female Fischer rats were divided into two groups: one exposed group (n=12) and one control group (n 12). The exposed group was given drinking water containing fructose (5% for 7 weeks, then 20% for 3 weeks). The control group was given tap water. Before sacrifice, whole body MRI was performed to determine volumes of total and visceral adipose tissue and lean tissue. MRI was performed using a clinical 1.5 T system and a chemical shift based technique for separation of water and fat signal from a rapid single echo acquisition. Fat signal fraction was used to separate adipose and lean tissue. Visceral adipose tissue volume was quantified using semiautomated segmentation. After sacrifice, a perirenal fat pad and the liver were dissected and weighed. Plasma proteins were analyzed by Western blot. Results: The weight gain was 5.2% greater in rats exposed to fructose than in controls (P=0.042). Total and visceral adipose tissue volumes were 5.2 cm(3) (P=0.017) and 3.1 cm(3) (P=0.019) greater, respectively, while lean tissue volumes did not differ. The level of triglycerides and apolipoprotein A-I was higher (P=0.034, P=0.005, respectively) in fructose-exposed rats.

The stochastic watershed is a segmentation algorithm that estimates the importance of each boundary by repeatedly segmenting the image using a watershed with randomly placed seeds. Recently, this algorithm was further developed in two directions: (1) The exact evaluation algorithm efficiently produces the result of the stochastic watershed with an infinite number of repetitions. This algorithm computes the probability for each boundary to be found by a watershed with random seeds, making the result deterministic and much faster. (2) The robust stochastic watershed improves the usefulness of the segmentation result by avoiding false edges in large regions of uniform intensity. This algorithm simply adds noise to the input image for each repetition of the watershed with random seeds. In this paper, we combine these two algorithms into a method that produces a segmentation result comparable to the robust stochastic watershed, with a considerably reduced computation time. We propose to run the exact evaluation algorithm three times, with uniform noise added to the input image, to produce three different estimates of probabilities for the edges. We combine these three estimates with the geometric mean. In a relatively simple segmentation problem, F-measures averaged over the results on 46 images were identical to those of the robust stochastic watershed, but the computation times were an order of magnitude shorter.

In this paper we introduce a minimum barrier distance, MBD, defined for the (graphs of) real-valued bounded functions f(A), whose domain D is a compact subsets of the Euclidean space R-n. The formulation of MBD is presented in the continuous setting, where D is a simply connected region in R-n, as well as in the case where D is a digital scene. The MBD is defined as the minimal value of the barrier strength of a path between the points, which constitutes the length of the smallest interval containing all values of f(A) along the path. We present several important properties of MBD, including the theorems: on the equivalence between the MBD rho(A) and its alternative definition phi(A); and on the convergence of their digital versions, (rho(A)) over cap and (phi(A)) over cap, to the continuous MBD rho(A) = phi(A) as we increase a precision of sampling. This last result provides an estimation of the discrepancy between the value of (rho(A)) over cap and of its approximation (phi(A)) over cap. An efficient computational solution for the approximation (phi(A)) over cap of (rho(A)) over cap is presented. We experimentally investigate the robustness of MBD to noise and blur, as well as its stability with respect to the change of a position of points within the same object (or its background). These experiments are used to compare MBD with other distance functions: fuzzy distance, geodesic distance, and max-arc distance. A favorable outcome for MBD of this comparison suggests that the proposed minimum barrier distance is potentially useful in different imaging tasks, such as image segmentation. 

In this paper we present an overview and summary of recent results of the minimum barrier distance (MBD), a distance operator that is a promising tool in several image processing applications. The theory constitutes of the continuous MBD in Rn, its discrete formulation in Zn (in two different natural formulations), and of the discussion of convergence of discrete MBDs to their continuous counterpart. We describe two algorithms that compute MBD, one very fast but returning only approximate MBD, the other a bit slower, but returning the exact MBD. Finally, some image processing applications of MBD are presented and the directions of potential future research in this area are indicated.

Purpose: To present and evaluate a whole-body image analysis concept, Imiomics (imaging omics) and an image registration method that enables Imiomics analyses by deforming all image data to a common coordinate system, so that the information in each voxel can be compared between persons or within a person over time and integrated with non-imaging data.

Methods: The presented image registration method utilizes relative elasticity constraints of different tissue obtained from whole-body water-fat MRI. The registration method is evaluated by inverse consistency and Dice coefficients and the Imiomics concept is evaluated by example analyses of importance for metabolic research using non-imaging parameters where we know what to expect. The example analyses include whole body imaging atlas creation, anomaly detection, and cross-sectional and longitudinal analysis.

Results: The image registration method evaluation on 128 subjects shows low inverse consistency errors and high Dice coefficients. Also, the statistical atlas with fat content intensity values shows low standard deviation values, indicating successful deformations to the common coordinate system. The example analyses show expected associations and correlations which agree with explicit measurements, and thereby illustrate the usefulness of the proposed Imiomics concept.

Conclusions: The registration method is well-suited for Imiomics analyses, which enable analyses of relationships to non-imaging data, e.g. clinical data, in new types of holistic targeted and untargeted big-data analysis.

Distance and path-cost functions have been used for image segmentation at various forms, e.g., region growing or live-wire boundary tracing using interactive user input. Different approaches are associated with different fundamental advantages as well as difficulties. In this paper, we investigate the stability of segmentation with respect to perturbations in seed point position for a recently introduced pseudo-distance method referred to as the minimum barrier distance. Conditions are sought for which segmentation results are invariant with respect to the position of seed points and a proof of their correctness is presented. A notion of δ-interface is introduced defining the object-background interface at various gradations and its relation to stability of segmentation is examined. Finally, experimental results are presented examining different aspects of stability of segmentation results to seed point position.