3DBGrowth: volumetric vertebrae segmentation and reconstruction in magnetic resonance imaging

This is a pre-print of an article published in Computer -Based Medical Systems . The final authenticated version is a v ailable online at: h https://doi.org/10.1109/CBMS.2019.00091 i . 3DBGr owth: volumetric v ertebrae segmentation and r econstruction in magnetic resonance imaging Jonathan S. Ramos + 1 , Mirela T . Cazzolato + , Bruno S. Faic ¸ al + , Marcello H. Nogueira-Barbosa ? , Caetano T raina Jr . + and Agma J. M. T raina + + Institute of Mathematics and Computer Science (ICMC), Univ ersity of S ˜ ao Paulo (USP). ? Ribeir ˜ ao Preto Medical School (FMRP), Univ ersity of S ˜ ao Paulo (USP). Abstract Segmentation of medical images is critical for making several processes of analysis and classification more reliable. W ith the gro wing number of people presenting back pain and related problems, the semi-automatic segmentation and 3D reconstruction of vertebral bodies became even more important to support decision making. A 3D recon- struction allows a fast and objecti ve analysis of each vertebrae condition, which may play a major role in surgical planning and ev aluation of suitable treatments. In this paper , we propose 3DBGro wth, which de velops a 3D recon- struction over the ef ficient Balanced Gro wth method for 2D images. W e also take advantage of the slope coefficient from the annotation time to reduce the total number of annotated slices, reducing the time spent on manual an- notation. W e show experimental results on a representative dataset with 17 MRI e xams demonstrating that our approach significantly outperforms the competitors and, on average, only 37% of the total slices with vertebral body content must be annotated without losing performance/accuracy . Compared to the state-of-the-art methods, we hav e achiev ed a Dice Score gain of over 5% with comparable processing time. Moreov er , 3DBGrowth works well with imprecise seed points, which reduces the time spent on manual annotation by the specialist. Key-w ords: 3D vertebrae reconstruction; magnetic resonance imaging; Balanced Gr owth . 1 Introduction Spinal diseases are increasing worldwide and can cause significant loss of function and compromise qual- ity of life. Surgical spinal treatments have been growing with the aging population, which requires accurate diag- nosis to av oid complications ( 1 ). Many spine patholo- gies can be detected and diagnosed using Magnetic Res- onance Imaging (MRI) exams ( 2 , 3 ). In a Computer - Aided Diagnosis (CAD) conte xt, the segmentation of each vertebra allows a faster and more objectiv e analysis of the vertebrae condition, aiding in the characterization and quantification of abnormalities ( 4 ). Moreo ver , an accurate se gmentation plays a major role and may assist the medical specialist in surgical planning and ev alua- tion of suitable treatments ( 5 ). The manual segmentation of a vertebral body in a slice-by-slice manner may be time-consuming and prone to errors, due to inter and intra-subject v ariabil- ity . Besides, the subjectiv e judgment that is employed may aggregate e ven more inaccuracy ( 6 ). Elseways, the knowledge gained ov er se veral years of expertise are in- corporated. Thus, the semi-automatic se gmentation as- sists the specialist, leads to time savings and reduces in- terpretation errors ( 7 ). The semi-automatic segmentation can be used in se v- eral analysis ( Figure 1 ). Quantitative measures can be extracted, such as semantic and agnostic features ( 8 ), consequently , machine learning techniques can be ap- C l a s s i f i c a t i o n Q u a n t i t at i ve V i s u a l i z a t i o n T r a i ni ng 2 D s e g m e n t a t ion & 3 D R e c on s t r u ct ion A n a l y s i s 2 D s l i c e - by - s l i c e a n n ot a t ion M R I E xa m S l i c e 1 , 2 , . . . , n Figure 1: Steps in a semi-automatic segmentation schema. plied for the classification of a gi ven anomaly ( 9 , 10 , 11 ) or for Content-Based Image Retriev al (CBIR) ( 12 , 13 ). Interactiv e se gmentation tools can be meaning- ful during the training and education of ne w radiolo- gists ( 14 ). Students can learn how to correctly segment each vertebra and to detect spine pathologies ( 15 ). This kind of training may a void potential medical failures, which reduces further complications. In general, the vi- sualization of 3D human structures can be used for sim- ulation of medical and surgical procedures ( 16 ). The GrowCut ( 17 ) method and its faster version, named as Fast GrowCut ( 18 ), which presents slightly lower segmentation accuracy , have been widely used in many medical MRI exams (especially in oncology) ( 8 ). The GrowCut method is based on cellular automata (analogous to a bacteria growth in biology) and works as a region-gro wing approach with an interactiv e label- ing procedure ( 17 ). 1 #1 #7 #4 M RI E x am I nt e r i o r A n n o t a t i o n A n n o t a t io n o f a f e w s lic e s S lic e s L5 E x t e r io r A n n o t a t io n 3 D B G r o w th I t e r a ti o n s I t e r a t io n 1 : D ic e 85. 3% I t e r a t io n 4 : D ic e 91. 8% I t e r a t io n 8 : D ic e 92. 8% I t e r a t io n 1 6 : D ic e 92. 9% Figure 2: Examples of slices annotation for a single vertebral body (Exam AKa2, L5) and 3DBGrowth's iterations. Ground- truth, interior and exterior annotation in red, magenta and blue, respecti vely . Sev eral fully automatic vertebrae segmentation meth- ods hav e been proposed ( 19 , 20 ). Ho wever , the y take too much processing time, which may not suit clinical practice ( 21 ). More recently , a novel approach called Balanced Growth (BGrowth) ( 22 ) has been proposed for the segmentation of crushed vertebral bodies in sin- gle slices. Briefly , BGrowth balances the weights along the gro wing path of a region, so that small intensities transitions are better delineated. The results achiev ed by BGro wth surpasses all methods from the literate, including Gro wCut. Moreov er , BGrowth is able to achiev e promising se gmentation results e ven with very simple/sloppy annotation (seed points). In this paper , we extrapolate the specialists' an- notation up to a fix ed limit without losing perfor - mance/accuracy , so that the total time spent on manual annotation is reduced. Moreover , we sho w how to ex- tend BGrowth to deal with the reconstruction of volu- metric exams (3D), introducing a no vel method called 3DBGrowth. The experimental results sho w that 3DB- Growth outperforms GrowCut, achieving an av erage Dice Score of 87% while managing comparable running time. Moreover , the method w orks well ev en with rough seed points, which reduces the time spent on manual an- notation. The remainder of the paper is structured as follows. In section 2 , we present 3DBGrowth for the segmenta- tion and reconstruction of vertebral bodies in volumet- ric MRI. Then, in section 3 we e xplore the materials and methods. Next, in section 4 , we detail the experimental design, results and discussion. Finally , section 5 draws the conclusions. 2 3DBGro wth: The proposed method The usual approach of annotating or stating seeds for segmenting medical images can be cumbersome for large 3D exams. Thus, this work main issue focuses on minimizing the human effort to segment and reconstruct 3D exams built on 2D slices. As illustrated in Figure 2 , depending on the MRI exam, not all slices have to be manually annotated by the user to process the 3D recon- struction. If the exams present a small spacing between slices (considering annotations on the sagittal plane), sev eral slices do not need to be annotated, once they are similar . This can be assessed by analyzing the negati ve slope coef ficient ( 23 ), which gi ves the best trade-off be- tween annotation time and performance measures, such as Dice Score Coefficient or Jaccard Coef ficient (better explored in the ne xt Section). Input: Image I and labels matrix L . Output: Se gmented binary image L == 1. 1 W ( L 6 = 0) ← 1 . 0 // Initial weights 2 for ∀ ( i, j, z ) do // For every voxel 3 for ∀ ( i n , j n , z n ) do // and its Neighbors 4 s ← W ( i, j, z ) ×  1 − | I ( i,j,z ) − I ( i n ,j n ,z n ) | max ∀ i,j,z I ( i,j,z )  5 if s > W ( i n , j n , z n ) then 6 W ( i n , j n , z n ) ← ( W ( i n , j n , z n ) + s ) / 2 7 L ( i n , j n , z n ) ← L ( i, j, z ) Algorithm 1: 3DBGrowth method o vervie w . The slope between two points, { x 1 , y 1 } and { x 2 , y 2 } , can be calculated by ∆ y ∆ x = y 2 − y 1 x 2 − x 1 , which is the rate of change between the two points. When the slope between two values of annotation time gets close to a straight horizontal line, there is no gain in annotation time, in other words, the closer the slope gets to 0, the lo wer the annotation time gain. Moreov er , by using a seg- mentation approach that does not require detailed in- terior/exterior annotation, such as BGro wth, the total time spent on annotation is greatly diminished. In addi- tion, BGrowth generally requires a simple rectangle-lik e annotation for the segmentation of individual vertebral bodies. For example, only 3 out of 7 slices were anno- tated in Figure 2 . In a verage, each slice took 6.5 sec- onds for annotation and 3DBGro wth took 0 . 64 seconds to process all 7 slices with only 16 iterations. Summing up, the whole process took 3 × 6 . 5 + 0 . 65 = 20 . 65 sec- onds and achiev ed a result close to the Ground-T ruth. In our proposed 3DBGro wth method (Algorithm 1 ), we initially consider the segmentation of foreground and background in gray-scale images. That is, considering a digital image I and its annotations/labels as a matrix L , both with dimension M × N × Z , representing the number of rows, columns and slices, respectively . Each entry in L has value − 1 (background), 0 (unlabelled) or 1 (foreground). Initially , each entry in a weight matrix W (with the same dimensions as I and L ) is set to 1 . 0 for seeds 2 T able 1: Summary of measures/methods used in this work. Symbol/Acronym Description DS C Dice Score Coefficient J AC Jaccard Coefficient H D Hausdorf f's distance GC GrowCut BG 3D Balanced Growth points and 0 otherwise (line 1). Then, for ev ery voxel ( i, j, z ) and each one of its 26 neighbours ( i n , j n , z n ) , a strength factor s is calculated (line 4). Here, the abso- lute intensity dif ference is normalized by the maximum intensity in the image and shifted by 1. Finally , s is mul- tiplied by the current weight W ( i, j, z ) , which produces values within [0 , 1] . If the strength s is greater than the neighbour's strength ( W ( i n , j n , z n ) , line 5), then the neighbour's strength is averaged with the new strength s (line 6) and its label recei ves the label of the voxel ( i, j, z ) (line 7). This process repeats until the algorithm con verges or for a fixed number of iterations defined by the user . 3 Materials and methods The methods and measures used for comparison, as well as the computational set-up and image dataset are described as follows. 3.1 Image Dataset Due to space limitations, only a meaningful dataset is presented herein, which comprises 17 anonymized MRI e xams, ranging from the sacrum (S1) to the mid thoracic (T6-T12) with corresponding manual segmen- tations. The exams present sev eral health conditions, such as scoliosis, spondylolisthesis and crushed verte- bra. The e xams have 3 . 24 ± 0 . 36 mm of slice thickness and 3 . 87 ± 0 . 36 mm of spacing between slices. More information and full access to the dataset is av ailable at ( 5 ). 3.2 Segmentation methods In order to e valuate the performance of 3DBGrowth (BG) in a 3D scenario, we compared it with Gro wCut (GC), which has been widely used for the task of ver - tebrae se gmentation ( 7 ). Since Fast GrowCut is an ap- proximation of the original GrowCut, presenting a lower accuracy ( 18 ), we consider only GrowCut on the exper - iments. Due to the limited number of samples (exams) no deep-learning approach was applied. 3.3 Comparison measures The Jaccard Coef ficient ( J AC ), Dice Score Coeffi- cient ( D S C ) and Hausdorff's Distance ( H D ) in vox- els ( 24 , 25 ) were considered. The Jaccard ( J AC ) calcu- lates the intersection of the manual and semi-automatic segmentation, and divides it by the union of them. This indicates the similarity between the segmentations, in which 0 indicates no similarity and, the closer J AC is to 1, the more alike the segmentations ( 26 ). The Dice ( D S C ) measures the spatial overlap of se veral segmen- tations of the same object, i.e, quantifies the overlap de- gree between two segmented objects. A DS C close to 0 indicates very lo w ov erlap, while a D S C closer to 1 indicates a higher overlap. In contrast, the Hausdorf f's Distance ( H D ) indicates how f ar a way (in voxels) the manual and semi-automatic segmentations are. A H D of 0 indicates comparable segmentations. T able 1 shows a summary of the segmentation meth- ods and comparison measures used in this work. (a) Original (b) Ground-T ruth (c) Annotation Figure 3: Example of sloppy annotation for a few vertebral bodies in one slice (Aka2, slice 8): ground-truth, interior and exterior annotations in red, magenta and blue, respecti vely . 3.4 Computational set-up The e xperiments were performed on a 2.40GHz In- tel(R) Core(TM) i7 CPU and 8GB RAM machine, using Matlab(R) version 2018a. The maximum number of it- erations was set to 50 for GrowCut and 3DBGrowth. No pre or post-processing technique were applied to assure the same conditions for all segmentation methods. 4 Experiments, results and discussion In our experimental design, we analyzed four main parts are: (A) the performance of each segmentation method is assessed using the whole exam; (B) each se g- mentation method is tested v arying the number of slices annotated for each exam; (C) the vertebral bodies are segmented one-by-one by each method; (D) a statistical test is applied to detect any significant difference be- tween the results of the two methods. 4.1 Exam segmentation analysis The initial interior and exterior annotation were per - formed in a “slopp y” way , i.e., no detailed boundary for accentuated curv es were drawn. In general, the anno- tation looks like a rectangle for the background and a simple line for the foreground ( Figure 3 ). For this exper- iment, this annotation has been performed on each slice on every exam and, to diminish computational process- ing, each exam is cropped using the con vex hull of the exterior annotation. T able 2 sho ws the av erage Dice Score ( DS C ), Jac- card ( J AC ) and Running T ime ( RT ) in seconds for each one of the 17 exams in the dataset. 3DBGro wth (BG) presented on a verage 81% DS C and 68% J AC while Gro wCut (GC) presented 76% and 61%, respec- tiv ely . Thus, BG presented higher D S C and J AC per- centages than GC for all exams, achieving up to 5% and 7% of DS C and J AC gain, respecti vely . Moreov er , considering DS C and J AC , BG's standard de viation is slightly lo wer . Analyzing the Running T ime ( RT ), very often, BG presented a lower average processing time than GC. 3 T able 2: Dice Score ( D S C ), Jaccard ( J AC ) and Running T ime ( RT ) in seconds for 3DBGrowth (BG) and Gro wCut (GC), considering all slices on each exam (volumetric). The best results are highlighted in bold. Exam DS C (%) J AC (%) RT (s) (#slices) BG GC Gain BG GC Gain BG GC DzZ T1 (12) 85 80 4.86 74 67 7.0 18 21 DzZ T2 (12) 82 77 4.2 69 63 5.8 27 31 AKa2 (15) 82 77 5.17 69 62 7.1 27 27 AKa3 (15) 78 73 4.78 64 58 6.2 27 29 AKa4 (15) 80 73 7.10 67 58 9.4 26 27 AKs5 (15) 84 78 6.54 73 63 9.2 23 24 AKs6 (15) 84 79 5.44 73 65 7.8 21 24 AKs7 (15) 80 73 7.6 67 57 9.9 21 24 AKs8 (15) 81 78 3.39 68 64 4.7 18 21 S01 (16) 85 82 2.91 74 70 4.3 44 50 S02 (16) 83 78 4.97 70 63 6.9 26 32 F02 (18) 78 74 3.63 64 59 4.7 48 55 St1 (20) 83 80 2.73 71 67 3.9 61 67 F04 (23) 78 75 3.42 64 60 4.5 13 14 AKs3 (25) 80 73 6.42 66 58 8.4 40 37 F03 (25) 80 77 3.57 67 62 4.8 08 09 C002 (31) 71 65 5.85 55 48 6.7 16 14 Mean 81 76 4.9 68 61 6.6 27 30 Std. dev . 3.4 3.9 1.5 4.7 5.0 1.9 13.7 15.2 Considering that the manual annotation of e very slice in the exam is too time consuming (for this dataset, on av erage, 11 minutes/exam), we conducted an experi- ment to v alidate the performance of 3DBGrowth and GrowCut when not all slices are annotated, as explored in the next section. 4.2 V ariation on the number of annotated slices W e used the previous experiment's annotations and left a few slices without annotation: we defined a slice distance, which manages the number of non-annotated slices between two annotated slices. For e xample, a slice distance of 0 implicates no slice is left without an- notation. The slice distance started at 0, increased by 1, up to 7. As the slice distance increases ( Figure 4 ), the a ver - age annotation time decreases and the processing time keeps almost steady for both methods. Also, D S C and J AC drops slo wly for both methods. Ho wev er , BG pre- sented best results than GC for both measures. Consid- ering the negati ve slope coefficient (as discussed in Sec- tion 2 ), highlighted over the magenta line, by using a threshold of -1, the best slice distance would be 3, which presents the best trade-off between annotation time and D S C / J AC . In the next Section, we conduct experiments using an- notations for individual v ertebral bodies. 4.3 Individual vertebrae segmentation T o speed-up the annotation process, we have consid- ered a slice distance of three for this experiment. Each vertebral body was annotated separately , as exemplified in Figure 5 . In general, both the interior and the exterior annotation looks like a rectangle and no detailed borders were drawn. As reported in T able 3 , GC and BG presented equal mean Running T ime ( RT ) and BG presented better mean DSC, J A C and HD than Gro wCut. Figure 6 de- 0 1 2 3 4 5 6 7 Annotated Slices Distance 0 1 2 3 4 5 6 7 8 9 10 11 12 Time (minutes) ( a ) An no tat ion Tim e Annotation Time Running Time (BGrowth) Running Time (GrowCut) -5.62 -1.9 -1.01 -0.34 -0.48 -0.64 -0.16 0 1 2 3 4 5 6 7 Annotated Slices Distance 0 1 2 3 4 5 6 7 8 9 10 11 12 Time (minutes) (b) Annotation Time Annotation Time Running Time (BGrowth) Running Time (GrowCut) 0 1 2 3 4 5 6 7 Annotated Slices Distance 49 54 59 64 69 74 79 84 89 Percentage (%) ( b ) DSC and J A C DSC (BG) DSC (GC) J A C (BG) J A C (GC) Figure 4: Quality comparison between 3DBGrowth and GrowCut ov er v ariations on the number of slices manually an- notated: (a) annotation time and running time results; (b) Dice ( D S C ) and Jaccard ( J AC ). (a) Original (b) Ground-T ruth (c) Annotation Figure 5: Example of seed points for a single vertebrae (St1, slice 10, L2): ground-truth (GT), interior and exterior annota- tions in red, magenta and blue, respectiv ely . T able 3: Comparison between 3DBGrowth (BG) and Grow- Cut (GC) for the Dice Score ( D S C ), Jaccard ( J AC ), Haus- dorff ( H D ) in vox els and Running T ime ( RT ) in seconds. The best values are highlighted in bold. DS C (%) J AC (%) H D (vox.) RT (s) V ertebrae BG GC BG GC BG GC BG GC T6 88 87 79 78 3.16 4.00 0.15 0.16 T7 85 83 73 69 78.8 79.1 7.95 6.77 T8 86 85 76 72 79.3 79.2 7.55 8.37 T9 81 80 50 52 80.0 79.9 7.83 8.38 T10 87 85 80 76 26.2 26.9 2.95 2.83 T11 86 84 77 73 6.09 6.99 0.91 0.88 T oracic T12 89 86 79 76 5.63 6.88 1.30 1.36 L1 89 87 78 76 6.56 7.31 1.57 1.56 L2 88 86 79 76 6.07 7.75 1.52 1.57 L3 86 85 75 72 6.40 7.49 1.68 1.83 L4 88 86 76 74 7.16 7.65 1.77 1.88 Lumbar L5 87 85 76 74 7.04 8.42 2.33 2.39 Sacral S1 88 86 79 76 6.18 7.57 1.74 1.88 Mean 87 85 77 74 7.24 7.72 1.52 1.52 Std. Dev . .07 .06 .08 .08 4.85 5.00 1.27 1.27 picts the results for a single vertebral body: BG achiev ed the highest D S C and the lowest H D . GC presented 4 T able 4: Comparison of the number of annotated slices, con- sidering a slice distance of three. Slices out of (v erte- AN T V ertebrae annotated bral content) (seconds) T6 3 . 0 ± . 00 7 . 0 ± . 00 28 . 7 ± . 00 T7 3 . 0 ± . 00 7 . 0 ± . 00 32 . 5 ± . 00 T8 3 . 0 ± . 00 7 . 0 ± . 00 34 . 6 ± 11 . 6 T9 3 . 0 ± . 00 7 . 0 ± . 00 30 . 0 ± 6 . 2 T10 2 . 5 ± . 52 6 . 7 ± 3 . 2 25 . 9 ± 7 . 1 T11 3 . 1 ± . 53 8 . 5 ± 2 . 6 30 . 2 ± 5 . 8 T oracic T12 3 . 6 ± . 50 9 . 6 ± 1 . 9 34 . 5 ± 8 . 1 L1 3 . 9 ± . 78 10 . 2 ± 2 . 2 36 . 8 ± 9 . 2 L2 4 . 2 ± . 75 10 . 9 ± 2 . 3 38 . 6 ± 10 . 1 L3 4 . 3 ± . 86 11 . 6 ± 2 . 1 40 . 0 ± 9 . 5 L4 4 . 5 ± . 62 12 . 5 ± 2 . 8 39 . 3 ± 6 . 3 Lumbar L5 4 . 5 ± . 72 12 . 5 ± 3 . 0 39 . 8 ± 7 . 8 Sacral S1 4 . 1 ± . 70 10 . 9 ± 3 . 3 35 . 8 ± 6 . 3 Mean 4 . 1 ± . 84 10 . 9 ± 2 . 9 35 . 9 ± 8 . 8 Annotated 37% spiculated borders, while BG presented smooth borders (closer to the ground-truth). Analyzing the a verage number of annotated slices per vertebra (T able 4 ), for this dataset, in av erage, only 37% of the total slices with vertebral content were annotated, which speeded-up the annotation process and took, in av erage, 36 seconds to annotate each vertebral body . (a) Ground-T ruth (b) Annotation (c) 3DBGrowth (d) GrowCut Figure 6: Comparison of results for L2 on exam AKa2: three slices, out of 7, were annotated. T o further inv estigate the results presented in T able 3 , we conducted a statistical test, as detailed next. 4.4 Statistical testing Considering that the resulting values of each mea- sure had several similar values, the Kolmogoro v- Smirnov ( 27 ) test was applied to verify the normality of the data. As the null hypothesis that the data follows a normal distribution was rejected for all measures, the W ilcoxon ( 28 ) test was used to analyze if there were significant statistical differences. In this test, the null hypothesis is that data from two dependent samples, e.g. the Dice Score ( D S C ) from 3DBGrowth (BG) and GrowCut (GC), were selected from populations having the same distribution, against the opposite alternati ve. In the W ilcoxon test results, 3DBGro wth presented significantly better Dice ( D S C ), Jaccard ( J AC ) and Hausdorf's Distance ( H D ) than Gro wCut. For the Run- ning Time ( RT ), there was no significant difference, which implicates that both methods presented compa- rable processing time. 5 Conclusion The semi-automatic segmentation of v ertebral bodies in a volumetric scenario is a challenging task, due to the large number of slices in the exams. T o obtain a proper 3D reconstruction of the vertebrae, one has to pay at- tention on allowing a fast and accurate segmentation of slices. W e ha ve in vestigated this challenge and used the slope coefficient of the annotation time, so that the spe- cialists' annotations were extrapolated from a slice to its neighbours up to a gi ven limit without losing accuracy and, at the same time, reduced the total time spent on manual annotation. On the dataset used, on av erage, only 37% of the slices with vertebral body content had to be annotated, consequently making the process faster (on average, 36 seconds for each vertebral body). W e have proposed 3DBGrowth method, which significantly outperforms GrowCut and k eeps comparable running time. More- ov er , 3DBGrowth presented the best results e ven with simple/sloppy seed points, which demands less ef fort on the annotation process. Acknowledgment This study was financed in part by the Coordenac ¸ ˜ ao de Aperfeic ¸ oamento de Pessoal de N ´ ıvel Superior - Brasil (CAPES) - Finance Code 001 and grant No.: 0487/17083480, by the S ˜ ao Paulo Research Founda- tion (F APESP , grants No. 2016/17078-0, 2017/23780- 2, 2018/06228-7, 2018/24414-2), and the National Council for Scientific and T echnological De velopment (CNPq). References 1 FEHLINGS, M. G. et al. The aging of the global populationthe changing epidemiology of disease and spinal disorders. Neur osur gery , v . 77, n. 1, p. 1–5, 2015. 2 RAK, M.; T ¨ ONNIES, K. D. On computerized methods for spine analysis in MRI: a systematic review . Int. J. Comput. Assist. Radiol. Sur g. , v . 11, n. 8, p. 1445–1465, Aug 2016. ISSN 1861-6429. 3 W ANG, Y . X. J. et al. Identifying osteoporotic vertebral endplate and cortex fractures. Quant Imaging Med Surg , v . 7, n. 5, p. 555–591, Oct 2017. 4 HAMMERNIK, K. et al. V ertebrae segmentation in 3D CT images based on a v ariational framework. In: Y A O, J. et al. (Ed.). Recent Advances in Computational Methods and Clinical Applications for Spine Imaging . Cham: Springer International Publishing, 2015. p. 227–233. ISBN 978-3-319-14148-0. 5 DZEN AN, Z. et al. Robust detection and segmentation for diagnosis of vertebral diseases using routine MR images. Computer Graphics F orum , v . 33, n. 6, p. 190–204, 2014. 6 GILLIES, R. J.; KIN AHAN, P . E.; HRICAK, H. Radiomics: images are more than pictures, they are data. Radiology , v . 278, n. 2, p. 563–577, Feb 2016. 5 7 EGGER, J.; NIMSKY , C.; CHEN, X. Vertebral body segmentation with GrowCut: Initial experience, workflo w and practical application. SA GE Open Med , v . 5, p. 1–5, 2017. 8 JUNIOR, J. R. F . et al. Radiomics-based features for pattern recognition of lung cancer histopathology and metastases. Computer Methods and Pr ograms in Biomedicine , v . 159, p. 23 – 30, 2018. ISSN 0169-2607. 9 CASTI, P . et al. Cooperative strategy for a dynamic ensemble of classification models in clinical applications: the case of MRI vertebral compression fractures. International Journal of Computer Assisted Radiology and Surgery , v . 12, n. 11, p. 1971–1983, Nov 2017. 10 FRIGHETT O-PEREIRA, L. et al. Shape, texture and statistical features for classification of benign and malignant vertebral compression fractures in magnetic resonance images. Computers in Biology and Medicine , v . 73, p. 147 – 156, 2016. ISSN 0010-4825. 11 CAZZOLA TO, M. T . et al. dp-breath: Heat maps and probabilistic classification assisting the analysis of abnormal lung regions. Computer Methods and Pro grams in Biomedicine , v . 173, p. 27–34, 2019. ISSN 0169-2607. 12 XUE, Z. et al. Spine X-ray image retriev al using partial vertebral boundaries. In: 2011 24th International Symposium on Computer-Based Medical Systems (CBMS) . [S.l.: s.n.], 2011. p. 1–6. ISSN 1063-7125. 13 GUR URAJ AN, A. et al. On the creation of a segmentation library for digitized cervical and lumbar spine radiographs. Computerized Medical Imaging and Graphics , v . 35, n. 4, p. 251 – 265, 2011. ISSN 0895-6111. 14 KARIMI, D. et al. Prostate segmentation in MRI using a conv olutional neural network architecture and training strategy based on statistical shape models. Int. J. Computer Assisted Radiology and Sur gery , v . 13, n. 8, p. 1211–1219, 2018. 15 STEF AN, P . et al. A radiation-free mixed-reality training en vironment and assessment concept for C-arm-based surgery . International J ournal of Computer Assisted Radiology and Sur gery , v . 13, n. 9, p. 1335–1344, Sep 2018. ISSN 1861-6429. 16 B ANERJEE, P . et al. A semi-automated approach to improv e the efficiency of medical imaging segmentation for haptic rendering. Journal of Digital Imaging , v . 30, n. 4, p. 519–527, Aug 2017. ISSN 1618-727X. 17 VEZHNEVETS, V .; K ONOUCHINE, V . GrowCut - interactiv e multi-label N-D image segmentation by cellular automata. International Conference on Computer Graphics and V ision - GraphiCon , v . 1, Nov 2005. 18 ZHU, L. et al. An effecti ve interactiv e medical image segmentation method using Fast GrowCut. In: . [S.l.: s.n.], 2014. v . 17. 19 K OREZ, R. et al. Model-based segmentation of vertebral bodies from MR images with 3D CNNs. In: OURSELIN, S. et al. (Ed.). Medical Image Computing and Computer-Assisted Intervention – MICCAI 2016 . Cham: Springer Int. Publishing, 2016. p. 433–441. ISBN 978-3-319-46723-8. 20 GA ONKAR, B. et al. Multi-parameter ensemble learning for automated vertebral body segmentation in heterogeneously acquired clinical MR images. J. of T ranslational Engineering in Health and Medicine , v . 5, p. 1–12, 2017. ISSN 2168-2372. 21 HILLE, G. et al. V ertebral body segmentation in wide range clinical routine spine MRI data. Computer Methods and Pro grams in Biomedicine , v . 155, p. 93 – 99, 2018. ISSN 0169-2607. 22 RAMOS, J. S. et al. BGrowth: an efficient approach for the segmentation of vertebral compression fractures in magnetic resonance imaging. Symposium on Applied Computing , p. 1–8, April 2019. 23 V ANNESCHI, L. et al. Fitness clouds and problem hardness in genetic programming. In: SPRINGER. Genetic and Evolutionary Computation Confer ence . [S.l.], 2004. p. 690–701. 24 J A CCARD, P . The distribution of the flora in the alpine zone. New Phytologist , v . 11, n. 2, p. 37–50, fev . 1912. 25 SØRENSEN, T . A Method of Establishing Groups of Equal Amplitude in Plant Sociology Based on Similarity of Species Content and Its Application to Analyses of the V e getation on Danish Commons . [S.l.]: I kommission hos E. Munksgaard, 1948. (Biologiske skrifter). 26 B ARBIERI, P . D. et al. V ertebral body segmentation of spine MR images using Superpixels. In: JUNIOR, C. T . et al. (Ed.). 28th IEEE International Symposium on Computer-Based Medical Systems . S ˜ ao Carlos and Ribeir ˜ ao Preto, Brazil: Conference Publishing Services (CPS), 2015. p. 44–49. ISSN 1063-7125. 27 MASSEY , F . J. The Kolmogorov-Smirnov test for goodness of fit. J ournal of the American Statistical Association , American Statistical Association, v . 46, n. 253, p. 68–78, 1951. 28 WILCO XON, F .; KA TTI, S.; WILCOX, R. Critical values and probability le vels for the W ilcoxon rank sum test and the W ilcoxon signed rank test. Selected T ables in Mathematical Statistics , v . 1, p. 171–259, 1970. 6