atrial fibrillation ( af ) affects approximately 2.3 million people in the usa with significant comorbidity and mortality , . it is a condition that increases the risk of stroke by a factor of six - fold and doubles the mortality rate of patients when compared to age - matched controls . since it was shown that ectopic beats from the pulmonary veins ( pv ) give rise to af   the treatment of af using radiofrequency catheter ablation ( rfca ) has become an important and common procedure . in this procedure , ablation lesions are created in a circular fashion around the pv ostia to electrically isolate the pvs , and thus the ectopic focal points , from the rest of the left atrium ( la ) . this treatment can provide a cure for the majority of patients and prevent the requirement for long - term pharmacotherapy . however , for a high proportion of patients ( 15%46% )  , there is recurrence of af . this normally requires a second or third re - do ablation procedure and thus has a high burden on health care . it is important to select patients who will respond better to rfca to reduce recurrence rates . several studies have shown that it is possible to predict the outcome of rfca procedures from the fibrosis extent in la . a scoring system based on the degree of fibrosis has been developed , leading to treatment stratification . other recent studies have also highlighted the significance of the extent of fibrosis or scar in la post - ablation for predicting outcome , evaluate effectiveness of ablation technologies   and helping to gain a better understanding of the left atrial substrate . in this context , magnetic resonance imaging ( mri ) has been shown to be effective for non - invasive imaging of the la . in particular , gadolinium delayed - enhancement ( de ) mri has the ability to detect changes that take place in the la both pre- and post - ablation and recent studies have shown that it could potentially be useful for selecting suitable candidates for rfca . de - mri is acquired with an inversion - recovery gradient echo sequence performed after administration of gadolinium yielding an image at an inversion time which is chosen to null the signal from healthy myocardium . due to the differential washout kinetics of gadolinium , scar or fibrotic areas are differentiated from heatlhy tissue . fibrotic or scar tissues in the myocardium appear with a signal intensity ( si ) above normal myocardium . 1 shows some examples of de - mri with intensities significantly higher than myocardium . quantification of scar or fibrosis from de - mri is challenging due to various reasons . the thin myocardium of the la wall leads to low singal - to - noise ratio . contrast variation in these images can be an issue due to choice of inversion time . also the complex geometry of the la results in some transverse slices where a very small section of the anatomy is visible , making manual quantification in these areas highly observer - dependent . finally , patients suffering from af often have an irregular heart rate and breathing making it hard to acquire good quality respiratory- and cardiac - gated images . quantification from such images become difficult to automate and manual quantification tends to be highly observer - dependent . in this work , the method exploits a well - known image segmentation approach known as graph - cuts . segmentation is achieved using a combination of scar intensity model priors and gaussian - fitting to tissues in the unseen image to be segmented . quantification and segmentation of ventricular scar from de - mri images have been studied in several investigations . refer to table i for a brief summary . a common method for detecting scar or fibrosis is to use a fixed model of thresholding between two and six standard deviations ( sd ) above the mean intensity of healthy myocardium . this requires the user to manually outline remote or healthy myocardium . another common method is the full - width - at - half - maximum ( fwhm ) which sets scar to be intensities greater than 50% of manually outlined hyper - enhanced myocardium . other approaches exist to compute the threshold automatically   or by applying clustering , , or with graph - cuts . methods have been proposed for endocardial surface - based segmentation   and threshold - based volumetric segmentation , , . in , the maximum intensity projection ( mip ) of the de - mri si on the segmented la shell this technique has an important drawback : it is only a visualisation of intensities and thus not a segmentation technique with no volumetric segmentation as output . in , a volumetric segmentation of pre - ablation la fibrosis this has a disadvantage that the la wall is thin and thus its manual segmentation can have significant inter - observer variation . other methods have employed fixed models for pre - ablation fibrosis   and post - ablation scar   with variable thresholding . in summary , a fixed thresholding model can not handle all the different variabilities encountered in la de - mri and these are both from the varied internal factors ( size , distribution and heterogeneity of scar ) and varied external factors ( resolution , image noise , inversion time , surface coil intensity variation ) . the inversion time choice can generate the appearance of more or less scar , and change the appropriate scar threshold . we present a method for segmenting and thus quantifying la fibrosis in de - mri . it is based on a probabilistic tissue intensity model of de - mri data , which is derived from both training and the unseen data . it offers two advantages : 1 ) it does not require manual outlining of base - line healthy myocardium , and 2 ) it provides greater accuracy than fixed models with no inter - observer variation . the algorithm was evaluated and compared with existing clinically - used methods using local pixel overlap measures . an abbreviated version of this work was published in   and . in this current version , we present the approach with more details including additional experiments and validation . we also include an automated adaptive step that allows for variation in the scar signal level and avoids sub - optimal scar intensity models . furthermore , we present a much more comprehensive validation of the algorithm on a larger clinical cohort . the algorithm was also used recently in a segmentation challenge , segmenting sixty de - mri datasets from three imaging centres . 15 patients were followed up at 6 months following their first ablation for the treatment of paroxysmal af . the procedures were carried out in the cardiac catheterization laboratory at st . thomas hospital , london , u.k . all patients gave written permission to take part in this local ethics committee approved study . a catheter was placed in the coronary sinus to provide a reference for electroanatomic mapping and to enable la pacing . two trans - 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 \end{document } reconstructed , 3 mins duration ) . data were acquired within a window of 150 ms every one rr interval , with a low - high k - space ordering and spatial pre - saturation with inversion recovery ( spir ) fat suppression . the ir time delay was determined from the look - locker sequence , and was set at an inversion time ( ti ) intermediate between the optimal tis to null myocardium and blood . slice orientation was in the four - chamber view for af ablation to optimize visualization of the pulmonary veins . typical respiratory gating efficiency is 50% but this varies considerably in this particular patient population . the inputs were a de - mri image and a segmentation of the la from an anatomical scan . the la segmentation was obtained from the b - ssfp whole - heart scan by an automatic approach based on a statistical shape model , and was followed where necessary by manual correction by a human rater ( throughout this paper , the terms human rater or observer refer to someone who has experience viewing tomographic images and can correctly identify the la endocardium and fibrosis in the la myocardium ) . the b - ssfp image was chosen over mra as it was acquired at the same phase in the cardiac cycle as the de - mri . the mra , though it provides better anatomical visualization , was not cardiac gated and it can be difficult to resolve the differences between this and the de - mri with registration . the anatomical images were registered to the de images using the dicom header data , and then refined by rigid and affine registration steps . the pipeline takes as input mri images and outputs binary segmentations ( rounded boxes ) . the pipeline takes as input mri images and outputs binary segmentations ( rounded boxes ) . segmentation of scars from de - mri images can be defined as assigning a label \documentclass[12pt]{minimal } 
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 } { } $ $ p({\bf i}\vert f_{p}=1)={{1}\over{\sqrt{2\pi\sigma^{2}}}}\exp\bigg [ -{{1}\over{2}}\bigg ( { { r-\mu}\over{\sigma}}\bigg)^{2}\bigg]\eqno{\hbox{(6)}}$$ 
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 } { } $ $ p({\bf i}\vert f_{p}=0)=\sum_{i=1}^{n-\{t\}}{{\mathhat{a}}_{i}}{\bf g}_{i}(\mu_{i},\sigma_{i})\eqno{\hbox{(8)}}$$ 
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 } { } $ ( a_{i},\mu_{i},\sigma_{i})$ 
 \end{document } were obtained using the expectation - maximization ( em)-algorithm . the number of tissue classes used was 4 pertaining to : blood pool , myocardium , scar and pericardial region . starting with an initial estimate of the mean and variance for the four classes , this was followed by a truncation of the distribution pertaining to scar . in summary , the algorithm extracted and incorporated knowledge both from the training dataset and the unseen image . the sc - bp contrast ratio was modelled from the training and intensity distributions of non - scar tissue were modelled from the unseen . this made the algorithm better equipped to handle contrast variations commonly encountered in de - mri . to ensure smoothness and avoid discontinuities in the final segmentation , the \documentclass[12pt]{minimal } 
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 } { } $ e_{{\rm prior}}$ 
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 } { } $ $ \varphi ( p , q)=1+{{1}\over{2}}\left({{\vert i_{p}-i_{q}\vert}\over{\sigma}}\right)^{2}\eqno{\hbox{(9)}}$$ 
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 } { } $ \sigma$ 
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 } { } $ $ \mu_{k+1}=\mu_{k}+\omega\cdot{\mathtilde\mu}_{k};\sigma_{k+1}=\sigma_{k}+\omega\cdot{\mathtilde{\sigma}}_{k}\eqno{\hbox{(10)}}$$ 
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 } { } $ ( \mu_{k},\sigma_{k})$ 
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 } { } $ \delta_{k}=({\mathtilde\mu}_{k+1}-{\mathtilde\mu}_{k})/{\mathtilde\mu}_{k}$ 
 \end{document}. the algorithm was evaluated on both numerical phantom and real patient mri datasets as described below . in the rest of the paper , the true location of scar the extent of scarring during ablation is non - deterministic and there is also confounding pre - ablation fibrosis . therefore , identifying locations where ablations were made is not sufficient to be a surrogate for the ground truth for scar . moreover , there is a high degree of inter- and intra - observer variability in manual segmentations of scar . the la geometry was extracted from a typical patient dataset . in the second step , this represented la wall . in a third step , regions were manually drawn within the constructed la wall ; these regions represented scar . in the final fourth step , intensities were sampled randomly from pre - determined distributions . these distributions belong to la wall and blood - pool , and are measured and obtained from real mri data . scar was filled with intensities from blood - pool but multiplied by a factor of 1.0 or above , and thus an sc - bp ratio of at - least 1.0 was maintained . this ratio emulated the selection of different inversion times for nulling the blood pool and was varied in experiments that follow . it is important to simulate partial voluming , anisotropic voxel sizes and noise in the phantoms . an anisotropic blur was applied with a kernel size of 2 mm in the through - plane direction and 1 mm in the in - plane direction . gaussian white noise \documentclass[12pt]{minimal } 
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 } { } $ ( \mu=0,\sigma=1)$ 
 \end{document } was added to the image . 4.images of a single - slice through a phantom taken at each stage of its construction process : ( a ) the phantom template with blood pool ( bp ) and atrial wall ( aw ) outlined semi - automatically using morphological dilation ; scar ( sc ) drawn manually . ( b ) assignment of intensity levels drawn randomly from pre - defined gaussian distributions , with separate distributions for each tissue class . ( c ) in - plane and through - plane blurring followed by the addition of gaussian white noise . images of a single - slice through a phantom taken at each stage of its construction process : ( a ) the phantom template with blood pool ( bp ) and atrial wall ( aw ) outlined semi - automatically using morphological dilation ; scar ( sc ) drawn manually . ( b ) assignment of intensity levels drawn randomly from pre - defined gaussian distributions , with separate distributions for each tissue class . ( c ) in - plane and through - plane blurring followed by the addition of gaussian white noise . numerical phantoms were generated by varying the sc - bp contrast ratio between 1.0 to 3.0 . this evaluated the algorithm 's performance on scar with varying contrast in relation to blood pool . the noise in the phantoms was maintained at signal - to - noise ( snr ) of 9.0 . training \documentclass[12pt]{minimal } 
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 } { } $ ( n=50)$ 
 \end{document } data sets were generated accordingly . to make training as realistic as possible , it was separately trained on sc - bp ratios : 1.51.8 and 1.82.1 . the algorithm was compared to ground - truth using the dice overlap co - efficient . 5.single slices through three different phantoms with numerically generated scars indicated by the arrows ( top row ) . sc - bp : ( a ) 1.4 , ( b ) 1.6 and ( c ) 1.8 . single slices through three different phantoms with numerically generated scars indicated by the arrows ( top row ) . sc - bp : ( a ) 1.4 , ( b ) 1.6 and ( c ) 1.8 . the segmentations from the algorithm are also shown ( bottom row ) . in a separate experiment , the snr was varied from 4 to 16 along with the sc - bp contrast ratios . a single instance of the algorithm was tested and this was trained on the sc - bp range 1.82.1 . in addition to the above experiments on scar enhancement and noise variation , the performance of the algorithm and fixed models ( fwhm and \documentclass[12pt]{minimal } 
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 } { } $ n$ 
 \end{document}-sd ) were compared on the same dataset . five separate phantoms were used from which 200 different scarred regions were identified and their sc - bp contrast ratio noted . the accuracy with each method segmented each of the 200 regions was measured with dice and reported . in these set of experiments , segmentations from the algorithm were compared to the combined manual segmentations of three observers . in addition to this , the algorithm was also compared to fixed models : fwhm and \documentclass[12pt]{minimal } 
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 } { } $ n$ 
 \end{document}-sd methods . training for the algorithm was accomplished using the leave - one - out principle , where 14/15 datasets were used for training and 1/15 used for testing . in the test scan , segmentation performance was measured both locally and globally for the image . for local comparison , performance on individual sections of scar was measured ( a total of 155 regions were considered ) and for a global comparison , total scar volume was measured . the pre - processing ( left atrium geometry extraction and registration ) was the same for each approach . they were combined to generate a consensus segmentation or pseudo - ground truth for each scan . the staple ground - truth was then be obtained by considering voxels to be scar if their probability is greater than 0.7 , or 70% . this is a reasonable threshold capable of generating a strong consensus segmentation ( in   the authors chose a lower consensus at 50% ) . to explore this threshold further segmentations were available from five experienced observers on a random subset of the clinical datasets . the segmentations were combined using staple and three thresholds were considered : 1 ) \documentclass[12pt]{minimal } 
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 } { } $ { \geq}{70\%}$ 
 \end{document}. this generated different consensus segmentations with varying degrees of consensus against which the algorithm 's performance was measured . finally , to further explore whether better training of the algorithm leads to better segmentations and thus better performance , different instances of the algorithm are evaluated by incrementing the number of training set . it is important to note that segmentations from the proposed algorithm were obtained without any user interaction necessary at any step of the algorithm . the most computationally demanding step was that of graph - cuts . on images of the resolution described above , the total running time of the proposed approach is less than a minute on a 2.5 ghz pc . to our experience the dice co - efficient of similarity is a well - known metric . it is given by:\documentclass[12pt]{minimal } 
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 } { } $ $ d={{2\vert x\cap y\vert}\over{\vert x\vert+\vert y\vert}}\times 100\eqno{\hbox{(11)}}$$ 
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 } { } $ \vert x\vert,\vert y\vert$ 
 \end{document } are total number of pixels in each region . the proportion of true positives and true negatives in the detection process was analyzed by means of receiver operating characteristic ( roc ) curves where possible . this is mostly how scar is quantified and interpreted in clinical studies   and also serves as an important indicator for the total scar burden on the atrium . fig . 6 show results from testing the algorithm on phantoms generated by varying the sc - bp contrast . the algorithm performs well within its training range with median dice \documentclass[12pt]{minimal } 
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 } { } $ 1.5\leq{\rm sc\hbox{-}bp}\leq 1.8 $ 
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 } { } $ 1.8\leq{\rm sc\hbox{-}bp}\leq 2.2 $ 
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 } { } $ { \rm sc\hbox{-}bp}\geq 3.0 $ 
 \end{document } is very difficult to achieve in practice . to summarise , this experiment evaluated the algorithm across a wide dynamic sc - bp contrast range and the algorithm 's approximation of ground truth was found to be good . 6.performance of algorithm on numerical phantoms with increasing sc - bp contrast and snr fixed at 9.0 . each graph is an instance of the algorithm : ( a ) trained on 1.5 to 1.8 , and ( b ) trained on 1.8 to 2.1 . boxes in the plot indicate the 9th , 25th , 50th , 75th and 91st percentiles . performance of algorithm on numerical phantoms with increasing sc - bp contrast and snr fixed at 9.0 . each graph is an instance of the algorithm : ( a ) trained on 1.5 to 1.8 , and ( b ) trained on 1.8 to 2.1 . boxes in the plot indicate the 9th , 25th , 50th , 75th and 91st percentiles . the algorithm is trained on datasets generated with sc - bp ranging between \documentclass[12pt]{minimal } 
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 \end{document } , this trend changes and all models perform equally well . fwhm and the algorithm perform consistently across the entire sc - bp range used in this experiment , with 3- and 4-sd models outputting less accurate segmentations on scar at certain sc - bp contrast levels ( 1.6 , 2.2 ) . this is because scar is not adequately segmented by 3- or 4-sd due to non - overlapping intensities between model and actual . these results highlight that the algorithm performs consistently on actual de - mri and across realistic sc - bp levels . assessment of performance using total scar volume reported by each method is important as this is mostly how scar is quantified and interpreted for clinical studies . results obtained from scar volume quantified by each \documentclass[12pt]{minimal } 
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 \end{document } of method is given in fig . each method was run three separate times with inputs ( i.e. , normal and hyper - enhanced myocardium ) fed from three independent observers . volume reported by each method was compared to the volume reported by three independent experienced observers ( see manual method in fig . all three runs of the algorithm produced the same result as depicted by the single bar in fig . this variation was primarily due to observer variability in selecting normal or hyper - enhanced tissue required for fixed models . this highlights that a standardized quantification for scar using a fixed model approach ( fwhm and sd ) can be difficult to achieve . segmentation quality was assessed by overlaying region contours over the original de - mri slices . it was generally observed that in images with excellent sc - bp contrast , contours followed scar boundaries accurately in both algorithm and fixed models . fixed models showed poor correlation when the sc - bp contrast is not sufficiently high . 16 where fwhm and the algorithm fared well with the algorithm providing a better approximation to the consensus segmentation . fixed models 3 and 6-sd have gross errors in their segmentations due to a large overlap of intensities between their scar model and actual healthy tissue . such segmentations are not usable for clinical studies and the operator would require to resort to threshold re - adjustment . the algorithm 's performance on a subset of clinical datasets was evaluated by varying the staple threshold and thus the level or strength of the consensus segmentation . there was a small difference in the algorithm 's performance noted when sc - bp contrast levels were low . with higher sc - when sc - bp contrast is poor , the consensus or agreement between observers can be low . by lowering the acceptable consensus threshold ( to 20% ) , dubious pixels are included in the ground truth where 2/10 observers would agree that it is scar . as the algorithm generally selects pixels which have close affinity to its models and priors , dubious pixels are omitted by the algorithm . each curve represents performance on consensus segmentations , with consensus varied from 20% ( weak ) to 70% ( strong ) . each curve represents performance on consensus segmentations , with consensus varied from 20% ( weak ) to 70% ( strong ) . the algorithm 's training set was incrementally increased and its segmentation overlap performance was noted . training had an impact on performance only when the training set and test set had similar sc - bp contrast levels . if these vastly differ , initial iterations of the algorithm generate poor segmentations and these progressively become better in later iterations when the scar intensity model is continuously adapted with feedback from previous iterations ( refer to  adapting training step in fig . each curve represents an instance of the algorithm trained on \documentclass[12pt]{minimal } 
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 \end{document}-sd method and the overall sensitivity and specificity is plotted for the parameter - less proposed algorithm and fwhm . 15.segmentations on clinical scans i : ( a ) original scan , ( b ) consensus staple segmentation , ( c ) algorithm , ( d ) fwhm , ( e ) 3-sd , ( f ) 6-sd . this scan has excellent sc - bp contrast and all methods except 3-sd and 6-sd demonstrate good accuracy . 16.segmentations on clinical scans ii : ( a ) original scan , ( b ) consensus staple segmentation , ( c ) algorithm , ( d ) fwhm , ( e ) 3-sd , ( f ) 6-sd . this scan has excellent sc - bp contrast and all methods except 3-sd and 6-sd demonstrate good accuracy . roc analysis of the algorithm , fwhm and \documentclass[12pt]{minimal } 
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 \end{document}-sd method and the overall sensitivity and specificity is plotted for the parameter - less proposed algorithm and fwhm . segmentations on clinical scans i : ( a ) original scan , ( b ) consensus staple segmentation , ( c ) algorithm , ( d ) fwhm , ( e ) 3-sd , ( f ) 6-sd . this scan has excellent sc - bp contrast and all methods except 3-sd and 6-sd demonstrate good accuracy . segmentations on clinical scans ii : ( a ) original scan , ( b ) consensus staple segmentation , ( c ) algorithm , ( d ) fwhm , ( e ) 3-sd , ( f ) 6-sd . this scan has excellent sc - bp contrast and all methods except 3-sd and 6-sd demonstrate good accuracy . in this work a segmentation algorithm was investigated for fast quantification of fibrosis in de - mri scans . the proposed algorithm offers the following advantages : 1 ) segments fibrosis without requiring a manual outline of remote or healthy myocardium . this is beneficial since remote myocardium tends to have low snr and manual selection suffers from high observer variability . 2 ) the algorithm does not routinely generate false positives as was observed in existing fixed model methods : fwhm and \documentclass[12pt]{minimal } 
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 \end{document}-sd . 3 ) the algorithm is developed particularly for left atrial fibrosis segmentation and all present approaches were developed for ventricle scans . 4 ) analysis of de - mri scans was shortened to an average of 30 seconds when compared to existing semi - automatic approaches requiring 2 minutes per scan on average . the algorithm along with existing approaches was tested on both numerical phantoms and clinical datasets . numerical phantoms provided with a wide dynamic range of variation in scar contrast otherwise not possible in clinical datasets . furthermore , in present literature , methods were validated on images using global overlap measures and not on individual regions and nor on individual sc - bp ratios . in this work , these together have allowed existing approaches to be investigated more thoroughly and results have revealed where they fail to perform . both fwhm and sd methods can have gross errors in its segmentations when scar contrast is not high enough causing significant overlap of intensities between the scar and healthy tissue . on the clinical datasets , the variability in scar volume from fwhm and sd when operated by three different experienced operators meant no standard quantification was possible . the algorithm reported the same volume in each run and this was also consistently found to be close to the consensus segmentation of experienced observers . the sc - bp contrast ratio is modelled from the training and intensity distributions of non - scar tissue is modelled from the unseen . these made the algorithm better equipped to handle contrast variations commonly encountered in de - mri . built - in smoothness constraints and the graph - cuts approach allow it to consider neighbouring regions for inclusion or exclusion even when they do not fit the model . the absence of ground truth for scar in de - mri is an important issue for segmentation methods and this has not been properly addressed in literature . one approach is to use voltage as a surrogate for scar . in this work , three experienced observers manually segmented scars in each de - mri scan . these were then combined to generate a consensus segmentation or pseudo - ground truth for each scan using a statistical approach . the degree of agreement of the consensus was also varied to show that a strong consensus was needed , especially when sc - bp levels were poor . a 70% threshold was overall deemed appropriate and this meant pixels with 7/10 consensus or above were included in the pseudo ground truth on which all tests were performed . furthermore , numerical phantoms are employed in this work to evaluate the algorithm , fwhm and sd over a wider dynamic range of sc - bp contrast ratios . the training step is also further explored in this work . a decrease in algorithm performance however , there might come a point where increasing the training set would not substantially increase the accuracy of the algorithm but this is dependent on the variation of the image population . the algorithm was evaluated using the leave - one - out approach , with 14/15 of the datasets used for training and 1/15 for testing . this would always be applicable with unseen data always being left out of the training and any previous data being added to the training . several recent studies  have highlighted the importance of quantifying la fibrosis in de - mri and these include its use in deciding treatment strategy and thus selecting patients who will respond better to rfca procedures . quantifying using fixed models such as fwhm and sd is frequently utilised clinically due to its simplicity . in this work the fwhm had overall equally low sensitivity and specificity than sd ; it is more reliable in segmenting scar with high sc - bp than low sc - bp . the sd fixed model was overall more sensitive with a higher true positive rate than fwhm , but this comes at the expense of reduced specificity . in scar detection , this is because rectifying quantified volumes by manually removing mis - labelled healthy pixels is relatively simpler and less time - consuming than manually labelling and including scar pixels that are missed . the algorithm is shown to have good true positive and true negative rates in the roc analysis , and higher than fwhm in all decision thresholds explored for sd . moreover , standardization is impossible to achieve in fixed models such as sd with several choices of thresholds left to the operator to tweak . the clinical translation of the proposed algorithm thus becomes clear  it aims to provide a reliable and standardized method of quantifying scar . quantification algorithms such as the one proposed , which can potentially be used in deciding treatment strategy , should be evaluated on a wide randomized spectrum of datasets from different imaging centres . to this end , the algorithm was recently evaluated in a segmentation challenge organized to compare quantification algorithms from seven different centres . the proposed algorithm generates binary images of scar and this can be mapped and represented on the segmented la surface model in two ways : 1 ) maximum intensity projection ( mip ) maps , and 2 ) probabilistic maps . the former can be used to visualise scar on la geometry and potential uses include predicting gaps in ablation patterns ( see fig . a recent algorithm   also allows them to be visualized on two - dimensional flattened maps of the la . gaps play an important role in reconnection of re - entrant circuits in af - cured patients . the latter can be used to obtain confidence levels on each region of scar extracted by the algorithm ( i.e. , a probability value between 0 and 1 of the chance of it being scar ) . an example of such a map can be seen in fig . 18 . 
 fig . 17.clinical applications i : two clinical cases with scar quantified by the algorithm and projected on left atrial surface using mip . 18.clinical applications ii : probabilistic map generated from the algorithm for three clinical cases ( p1 , p2 , p3 ) shown alongside maximum intensity projections ( mip ) of manually outlined scar . clinical applications i : two clinical cases with scar quantified by the algorithm and projected on left atrial surface using mip . clinical applications ii : probabilistic map generated from the algorithm for three clinical cases ( p1 , p2 , p3 ) shown alongside maximum intensity projections ( mip ) of manually outlined scar . one of the limitations of the study is the absence of ground truth in the clinical datasets . to overcome this consensus segmentations from three observers furthermore , numerical phantoms were used and ground truth was readily available in these cases . a second limitation is in the dice co - efficient used to measure overlap between segmentations . dice can be highly sensitive to small translational errors between the test and true regions . to overcome this , de - mri is becoming a preferred method for non - invasive imaging of myocardial scar . currently , sd and fwhm fixed thresholding models are frequently utilized clinically to quantify scar due to their simplicity . present literature has only evaluated these methods using global image measures and thus their deficiences could not be noted . in this work , there are two important contributions : 1 ) sd and fwhm fixed models are evaluated on individual regions of scar and thus various scar contrast ratios are examined to show they fail when some contrast levels do not suit the selected threshold in sd or 50% cut - off in fwhm . 2 ) the proposed algorithm has the potential to standardize quantification of scar from routine clinical scans ; it requires no threshold selection and is shown to be more sensitive and specific than sd and fwhm in scar detection . this could considerably reduce the recurrence rates , procedure risk and high financial burden associated with unsuccessful rfca treatment . patients not deemed appropriate for rfca based on their scar assessment could be treated far less invasively using drug therapy .
delayed - enhancement magnetic resonance imaging ( de - mri ) is an effective technique for detecting left atrial ( la ) fibrosis both pre and postradiofrequency ablation for the treatment of atrial fibrillation . 
 fixed thresholding models are frequently utilized clinically to segment and quantify scar in de - mri due to their simplicity . 
 these methods fail to provide a standardized quantification due to interobserver variability . 
 quantification of scar can be used as an endpoint in clinical studies and therefore standardization is important . in this paper 
 , we propose a segmentation algorithm for la fibrosis quantification and investigate its performance . 
 the algorithm was validated using numerical phantoms and 15 clinical data sets from patients undergoing la ablation . 
 we demonstrate that the approach produces good concordance with expert manual delineations . 
 the method offers a standardized quantification technique for evaluation and interpretation of de - mri scans .