{"responseHeader":{"status":0,"QTime":28,"params":{"q":"{!q.op=AND}id:\"712821\"","hl":"true","hl.simple.post":"","hl.fragsize":"5000","fq":"!embargo_tdt:[NOW TO *]","hl.fl":"ocr_t","hl.method":"unified","wt":"json","hl.simple.pre":""}},"response":{"numFound":1,"start":0,"docs":[{"ark_t":"ark:/87278/s6t75skd","setname_s":"ir_uspace","restricted_i":0,"department_t":"","format_medium_t":"application/pdf","creator_t":"Gerig, Guido","identifier_t":"uspace,19289","date_t":"2006-01-01","bibliographic_citation_t":"Xu, S., Styner, M., Davis, B., Joshi, S., & Gerig, G. (2006). Group mean differences of voxel and surface objects via nonlinear averaging. Proceedings of IEEE International Symposium on Biomedical Imaging (ISBI), 758-61.","mass_i":1515011812,"publisher_t":"Institute of Electrical and Electronics Engineers (IEEE)","description_t":"Building of atlases representing average and variability of a population of images or of segmented objects is a key topic in application areas like brain mapping, deformable object segmentation and object classification. Recent developments in image averaging, i.e. constructing an image which is central within the population, focus on unbiased atlas building with nonlinear deformations. Groupwise nonlinear image averaging creates images which appear sharper than linear results. However, volumetric atlases do not explicitely carry a notion of statistics of embedded shapes. This paper compares population-based linear and non-linear image averaging on 3D objects segmented from each image and compares voxel-based versus surface-based representations. Preliminary results suggest improved locality of group average differences for the nonlinear scheme, which might lead to increased significance for hypothesis testing. Results from a clinical MRI study with sets of subcortical structures of children scanned at two years with follow-up at four years are shown.","first_page_t":"761","rights_management_t":"(c) 2006 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.","title_t":"Group mean differences of voxel and surface objects via nonlinear averaging","id":712821,"publication_type_t":"pre-print","parent_i":0,"type_t":"Text","thumb_s":"/8e/20/8e20038b873a81d6ca31f452622f87d75bcc8090.jpg","oldid_t":"uspace 10837","metadata_cataloger_t":"CLR","format_t":"application/pdf","modified_tdt":"2015-02-17T00:00:00Z","school_or_college_t":"","language_t":"eng","issue_t":"758","file_s":"/d0/00/d000b1591431219f50b98d89f9d0c9ac2fb8414c.pdf","format_extent_t":"260,846 bytes","other_author_t":"Xu, Shun; Styner, Martin; Davis, Brad; Joshi, Sarang","created_tdt":"2015-02-17T00:00:00Z","_version_":1642982816963624960,"ocr_t":"GROUP MEAN DIFFERENCES OF VOXEL AND SURFACE OBJECTS VIA NONLINEAR AVERAGING Shun Xu1, Martin Styner1,2, Brad Davis1,3, Sarang Joshi1,3, Guido Gerig1,2 ∗ The University of North Carolina Departments of 1Computer Science, 2Psychiatry, 3Radiation Oncology Chapel Hill, NC 27599. xushun@cs.unc.edu ABSTRACT Building of atlases representing average and variability of a population of images or of segmented objects is a key topic in application areas like brain mapping, deformable ob-ject segmentation and object classification. Recent develop-ments in image averaging, i.e. constructing an image which is central within the population, focus on unbiased atlas build-ing with nonlinear deformations. Groupwise nonlinear image averaging creates images which appear sharper than linear re-sults. However, volumetric atlases do not explicitely carry a notion of statistics of embedded shapes. This paper compares population-based linear and non-linear image averaging on 3D objects segmented from each image and compares voxel-based versus surface-based representations. Preliminary re-sults suggest improved locality of group average differences for the nonlinear scheme, which might lead to increased sig-nificance for hypothesis testing. Results from a clinical MRI study with sets of subcortical structures of children scanned at two years with follow-up at four years are shown. 1. INTRODUCTION The construction of brain atlases is central to the understand-ing of the variabilities of brain anatomy. Most research has been directed towards the development of 3D brain atlases us-ing image mapping algorithms [1, 2] that can map and trans-form a single brain atlas onto a population. In this para-digm the atlas serves as a deformable template and the nonlin-ear transformations encode the variability of the population. Most recent work [3, 4] of nonlinear unbiased atlas build-ing avoids the bias introduced by template selection. Further, pairwise deformations are replaced by simultaneous group-wise estimations of the unbiased atlas and the transformations [5, 6]. Principal component analysis (PCA) has been applied di-rectly to the high dimensional dense deformation fields or to ∗We would like to thank Matthieu Jomier for the computation of the origi-nal brain deformation maps. The datasets were provided by the UNC Autism center and NIH grant RO1 MH61696. This research is supported by the NIH NIBIB grant P01 EB002779 and the UNC Neurodevelopmental Disorders Research Center HD 03110. the control points of the free-form deformation to study the variabilities of the deformation fields[7]. Robustness of this conventional linear method is highly reduced due to insuf-ficient training in practical settings[8]. Linear surface shape statistical methods can also be used to calculate average shapes and major modes of variation, such as PDM [9] and SPHARM [10]. This Euclidean framework has to be replaced by a non-linear Riemannian space framework when applied to nonlin-ear medial shape models [11]. But statistical shape properties derived from nonlinear deformation fields of atlases have not been sufficiently studied. The difference between linear and nonlinear voxel-based atlas building schemes clearly showed improved sharpness of the nonlinear method [6]. However, its advantage for statisti-cal analysis of shapes and hypothesis testing between groups has not yet been sufficiently explored. This paper describes work in progress that explores statis-tical properties of shape populations averaged via nonlinear deformations obtained by unbiased atlas building. Prelimi-nary results are shown as comparison of shape averaging via linear and nonlinear deformations, and as exploration of the potentials of nonlinear schemes in group discrimination and localization of population differences. 2. EXPERIMENTAL DESIGN In order to compare group differences of linear v.s. nonlin-ear shape averages, our shape analysis methods can be di-vided into four steps. First, 3D affine transformation and nonlinear unbiased groupwise registration[4] are applied to two groups of grey level brain images, respectively. Informa-tion of all transformations are retained. Second, binary voxel representation of subcortical structures are extracted from the same two groups of brain images, using semi-automatic user-supervised segmentation. Applying the corresponding trans-formations retained from step one to these binary segmenta-tions and averaging them result in linear and nonlinear aver-age images. Third, parameterized surface representations of anatomical brain structures are established based on the bi-nary segmentations in step two. Linear and nonlinear shape 0-7803-9577-8/06/$20.00 ©2006 IEEE 758 ISBI 2006 averages are derived by applying the affine transformations and the 3D deformation fields retained in step one to surface points followed by averaging the resulting transformed ob-jects. Finally, group differences are studied by both volumet-ric and surface comparisons. Fig. 1. Linear and nonlinear construction framework applied to MRI brain images. The construction framework depicted in Figure1 produces affine transformations {fi}Ni =1 such that fi : Ii → IAff i , where {Ii}Ni =1 are a population of N individual MRI images and {IAff i }Ni =1 are their corresponding affinely-transformed coun-terparts. Nonlinear diffeomorphic mappings hi : Ω → Ωi are then estimated to deform each IAff i into an unbiased atlas IAtlas[4, 6], where Ω ⊂ R3 and Ωi ⊂ R3 are the coordi-nate systems of IAtlas and IAff i respectively. Since each hi is a diffeomorphism[4], its inverse h −1 i : Ωi → Ω exists and can be calculated. In this study, two groups of 5 cases are selected over Time1 (2 years of age) and Time2 (4 years of age) from our autism study database. The above framework was then applied to obtain the linear affine transformations {fi}Ni =1 and nonlinear deformations {h −1 i }Ni =1, where N = 5. We started with gray-level MRI image deformations to obtain {fi}Ni =1 and {h −1 i }Ni =1, and then applied them to bi-nary voxel and surface segmentations. Thus we can study shape variability and group differences in different aspects and make comparison, which will be illustrate in the follow-ing sections. 3. VOXEL-BASED REPRESENTATION AND PROCESSING In this section we describe how to obtain linear and nonlinear probability maps. Anatomical structures were first segmented from MRI data using user-supervised segmentation by geo-desic snakes and then represented as binary voxel represen-tations. Each of the N MRI data Ii corresponds to T binary segmentations {Bij}Tj =1 of T brain structures. Each of the NxT segmentations Bij were affinely trans-formed into BAff ij by fi using trilinear interpolation, respec-tively. Averaging BAff ij over i gives us population probability maps for affine transformations, as shown in Figure2 (a). We then continued to deform BAff ij into Bdef ij using the deformation field h −1 i . Averaging Bdef ij over i gives us population proba-bility maps after nonlinear deformations, as shown in Figure2 (b). Fig. 2. Coronal view of combined objects illustrating ven-tricles, caudates, and amygdalae. Left: Probability map of linearly transformed segmentations of subcortical brain struc-tures. Right: Probability map of nonlinearly deformed seg-mentations. Note that the deformation fields {h −1 i }Ni =1 are obtained via fluid deformation between grey level volumetric images but without explicit notion of object boundaries. These de-formation fields are then applied to the embedded binary seg-mentations to validate the quality of atlas building. The re-sult in Figure 2 shows that linear averaging of voxel objects creates blurry probability maps, whereas nonlinear averages appear sharper. 4. SURFACE-BASED REPRESENTATION AND PROCESSING Voxel-based image averaging does not result in an explicit representation of average object boundaries and does not di-rectly express surface variability of anatomical structures. In this section, we therefore apply the set of linear and nonlinear transformations to object surface representations. After voxel segmentation, shapes were processed by an analysis pipeline that includes surface extraction and parame-trization using spherical harmonics[12, 10]. This parametric 759 boundary description is called SPHARM. Using a uniform icosahedral subdivision of the spherical parametrization gives us Point Distribution Models (PDM). PDM point correspon-dence over the whole population is defined by surface points with equivalent surface parameterizations. In our study, each of the MRI images Ii has T bound-ary models {Sij}T i=1, while each shape Sij has M = 1442 boundary points {Pijk}Mk =1 derived from the SPHARM de-scriptor. {Pijk}Ni =1 are corresponding points from parame-trization, which means point k of shape j corresponds to each other invariant to individual i. In this surface averaging process, original surface correspondences are propagated through all stages of deformations and can be used for object averaging. The affine transformations fi were applied to the points {{Pijk}Mk =1 }Tj =1 individually. Grouping all theM mean points ¯ PAff jk = 1 N N i=1 PAff ijk gives us a linear shape average ¯ Sj of structure j. Similarly, nonlinear deformation fields were ap-plied to allNxTxM points accordingly, and a nonlinear shape average ¯ Sdef was obtained. Note that {fi}Ni =1 and {h −1 i }Ni =1 applied to surface points are obtained via affine transforma-tion and fluid deformation between grey level volumetric im-ages. Fig. 3. Top: Colormaps of standard-deviation of surface points ploted on average shapes. Top left: Colormap of STDs of linearly transformed surface points. Top right: Colormap of STDs of nonlinearly deformed surface points. Bottom: Histograms of STDs correspond to the shape above. Putamen is chosen as an illustration example. Similar to a representation of a fuzzy boundary in voxel-based processing as a measure of \"sharpness\" of the popula-tion model, variability of a population is expressed by calcu-lating the standard-deviation of each surface point. In Figure 3, we see that the shape on the right depicts more blue region, which implies variability of nonlinearly de-formed surface corresponding points is in generally smaller; while on the left the image is more with green and red color, which implies bigger variability for linearly transformed sur-face corresponding points. While we gain intuitions by look-ing at the colormap of the STDs, the corresponding histogram and the table of statistical data are shown in Figure 3 and Ta-ble 1. Standard deviation statistics of putamen at Time1: Affine Nonlinear Mean 1.6816 1.1261 50 percentile 0.3311 0.1807 85 percentile 0.3759 0.2141 Table 1. Statistical data of the two histograms of standard de-viation shown in Figure 3. The data shows smaller variability of surface points in the nonlinear case. 5. GROUP DIFFERENCE ANALYSIS In this section we compares voxel-based and surface-based representations and explores group differences obtained via linear and nonlinear shape averaging. 5.1. Volumetric Analysis Between Groups The result in Figure2 shows that nonlinear averages of voxel objects appear sharper than averages done in a linear scheme. In order to assess linear and nonlinear methods in group dif-ference comparison, we compute probabilistic distance be-tween two groups Time1 v.s. Time2 by the following prob-ability overlap measure[13]: POV (A,B) = 1 − |PA − PB| 2 PAB Probabilistic distance: Time1 v.s. Time2 L. Caud R. Caud L. Put R. Puta Affine 0.85391 0.92314 0.79608 0.89028 Nonlinear 0.88659 0.92457 0.83059 0.85069 Table 2. Distances between probability maps of Time1 and Time2 , as shown in Figure2. Caudate and Putamen are cho-sen as illustration examples. As shown in table 2, distances of affine and nonlinear probability maps are very close. By looking at these num-bers of global probabilistic measurement, it is difficult to gain information of localization or intuitive conception. Volumet-ric analysis seems inefficient to address our problem of group comparison by different approaches, which motivates analy-sis via an explicit object representation. 760 5.2. Shape Mean Difference Analysis Between Groups With the goal of exploring whether the nonlinear scheme shows potentials to improve group discrimination, we compares the differences between group means calculated by both linear and nonlinear averaging. We applied the processing described in section 4 to two populations over two time points, respectively, and we obtain for each time point the surface-based group mean after affine registrations and that after nonlinear deformations. Compar-ing the group mean differences over time gives results on the left and middle in Figure 4. On the other hand, the voxel-based scheme described in section 3 gives us linear and non-linear probability maps, out of which we applied thresholding and surface extraction to obtain the surfaces of average voxel objects. Comparing them over time gives the result on the right in Figure 4. Fig. 4. Groupwise average model comparison shown for cau-date and putamen. Left column: mean difference between Time1 and Time2 after affine transformation. Middle: mean difference between Time1 and Time2 after nonlinear diffeo-morphic deformation. Right column: difference of boundary models extracted from threshold of Time1 and Time2 proba-bility maps. Figure 4 illustrates the mean shape difference color-coded on the surface. The illustrations suggest that mean differences are more distributed for the affine registrations and more con-centrated at specific regions for nonlinear. The average sur-face after nonlinear deformation (middle) and surface of av-erage voxel object (right) appear similar, as both represent objects obtained by nonlinear averaging but using a surface-based versus voxel-based processing. The above preliminary results are very interesting and sug-gested improved locality of group average differences for the nonlinear scheme, which intrigues our continuing work of hy-pothesis testing. 6. DISCUSSION In order to gain insights into the potential of a nonlinear scheme in improving localization of group differences, this paper dis-cusses the comparison of group mean differences of voxel-based and surface-based objects via linear and nonlinear av-eraging. We started with two populations represented as MRI images and its unbiased atlases, then applied the affine regis-trations and nonlinear diffeomorphic deformations to binary voxel and surface segmentations of subcortical structures, and studied the population mean differences. We make use of the notion of statistics of the embedded shapes to study the prop-erties of nonlinear atlas deformation fields, and explore its po-tentials in group discrimination. Our findings suggest better localization of group mean differences for nonlinear schemes and they provide ample motivation for the future shape differ-ence hypothesis testing in the non-linear deformation setting. 7. REFERENCES [1] A. W. Toga P. M. 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Schnabel, \"Automatic con-struction of 3d statistical deformation models using non-rigid registration,\" in MICCAI, 2001, pp. 77-84. [8] Z. Xue D. Shen B. Karacali and C. Davatzikos, \"Statistical rep-resentation and simulation of high-dimensional deformations: Application to synthesizing brain deformations,\" in MICCAI, 2005. [9] T. F. Cootes C. J. Taylor D. H. Cooper J. Graham, \"Active shape models - their training and application,\" in Computer Vision and Image Understanding, 1995, pp. 38-59. [10] Ch. Brechb¨uehler G. Gerig O. K¨ubler, \"Parametrization of closed surfaces for 3d shape description,\" in CVIU, 1995, pp. 154-170. [11] P.T. Fletcher C. Lu S.M. Pizer S. Joshi, \"Principal geodesic analysis for the study of nonlinear statistics of shape,\" in IEEE TMI, 2004, vol. 23, pp. 995-1005. [12] M. Styner J. A. Lieberman D. Pantazis G. Gerig, \"Boundary and medial shape analysis of the hippocampus in schizophre-nia,\" in MedIA, 2003, pp. 197-203. [13] G. Gerig M. Jomier M. Chakos, \"Valmet: A new validation tool for assessing and improving 3d object segmentation,\" in MICCAI, 2001, pp. 516-528. 761"}]},"highlighting":{"712821":{"ocr_t":[]}}}