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TMBE-00886-2006.R3
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A Novel 3D Image-based Morphological Method for Phenotypic Analysis Erika Kristensen, Trish E. Parsons, Benedikt Hallgrímsson, Steven K. Boyd ! Abstract—A new approach for the study of geometric morphometrics is presented based on well-established image processing techniques in a novel combination to support highthroughput analysis necessary for large scale determination of genotype-phenotype relationships. The method retains full threedimensional (3D) data, and avoids manual landmark selection. Micro-computed tomography images are superimposed into a common orientation by rigid image registration with an isotropic scale factor. An average sample shape is determined by averaging the intensities of corresponding voxels of the registered images, and shape variation is determined by calculating the image gradient of the average shape. Localized shape differences between mean images or between an individual and a group mean are identified and quantified by surface-to-surface distance measures of superimposed images. Validation was performed using geometric shapes of known dimensions as well as biological samples of C57BL/6J and A/WySnJ mouse skulls, and shape variation of the mouse skulls was consistent with previously published results. Although the image gradient is sensitive to both image registration and filtration of the average image, the effect can be minimized by consistent use of image analysis parameters. While the proposed approach deviates from well established landmark-based geometric morphometric tools, it is not intended to replace these current methods. Rather, it will be an important contribution to provide high-throughput screening in large-scale studies focused on understanding genotypephenotype relationships so that subsequent morphometric approaches using established techniques can be better focused. Index Terms— imaging, micro-computed morphometrics, phenotyping, shape
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tomography,
I. INTRODUCTION
URING the past decade, biology has been revolutionized by an enormous increase in the rate of
Copyright (c) 2006 IEEE. Personal use of this material is permitted. However, permission to use this material for any other purposes must be obtained from the IEEE by sending an email to
[email protected]. Manuscript received December 27, 2006. This work was supported in part by the Canadian Institutes of Health Research under Grant ITM-71877. E. Kristensen is with the Schulich School of Engineering, University of Calgary, Calgary, AB T2N1N4, Canada (email:
[email protected]) T. E. Parsons is with the Faculty of Medicine, University of Calgary, Calgary, AB T2N4N1, Canada (e-mail:
[email protected]). B. Hallgrímsson is an Associate Professor in the Faculty of Medicine, University of Calgary, Calgary, AB T2N4N1, Canada (e-mail:
[email protected]). S. K. Boyd is an Associate Professor at the Schulich School of Engineering, University of Calgary, Calgary, AB T2N1N4, Canada (phone: 403-220-4173; fax: 403-282-8406; email:
[email protected]).
knowledge growth in molecular and cellular biology. Conspicuously, the analysis of morphology has been largely unaffected by these sweeping changes. This is an important gap because as research designs in studies that link genetic perturbations to disease or developmental outcomes become increasingly multifactorial and complex, there is an increased need for a higher rate of throughput for refined analyses of morphological variation. In this paper, we propose a novel addition to the current morphometrics toolkit that will support the high rate of throughput necessary for large scale genotypephenotype correlations in developmental biology or the study of diseases with morphological manifestations. We classify this method as high-throughput because the rate of analysis is significantly increased as compared to current morphological methods. Shape is recognized as the geometric properties of an object that are invariant to location, scale and orientation [1, 2], and morphometrics is the field concerned with the quantification and comparison of shape [3]. Geometric morphometrics (GM) techniques use landmark coordinates to analyse shape, and are the most widely used methods of shape analysis [3-6]. The current gold standard for geometric morphometrics, Procrustes analysis, is classified as a superimposition method that factors out location, orientation and size to obtain the true shape of the object [7, 8]. However, there are inherent limitations associated with landmark-based analyses [5]. For example, only information on the landmarks is captured and analysed, and all information on the shape of the object between the landmarks is disregarded. Additionally, the process of identifying and recording numerous landmarks is time-consuming and involves significant user interaction. An alternative approach to landmark-based shape analysis is the construction of average shapes. This has been performed in the field of neuroanatomy through the creation of average brain atlases [9-13]. Several different registration methods have been utilized, including multi-modal image registration [9], inverse consistent linear elastic image registration [11], boundary mapping [14], and intensity-based nonrigid registration [13]. Voxel-based morphometry is a method used to identify volumetric differences in brain morphology accomplished through spatial normalization, image partitioning, smoothing and statistical analysis [15]. Another issue related to shape analysis is the ability to quantify changes through the comparison of a subject’s images to a control or baseline image from the same subject at an earlier time point [16, 17]. Here, we propose a high-throughput
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phenotypic analysis method using average shapes from 3D image data. Although the method will yield quantitative measures of shape variation, we intend to use this primarily as a screening tool so that established morphometric tools can be applied for further analysis.
II. METHODS All programs were written in the C++ language and integrate components from open source toolkits in a novel combination (Visualization Toolkit, VTK; Insight Segementation and Registration Toolkit, ITK). The method is demonstrated for analysis of image data from a microcomputed tomography (!CT) scanner, but the approach is not limited to this modality, and may be applicable to 3D images obtained from media where image intensity is well calibrated. To visualize the images, a marching cubes algorithm is used to construct surfaces at a desired isosurface value [18], as chosen through inspection of image histograms of voxel intensities to separate the data of interest from the background. A. Registration Image registration was used to find the transform for each image in a given cohort to a fixed image (3 rotations, 3 translations and isotropic scale). We used an intensity-based rigid registration with a Mattes mutual information metric, a linear interpolator and a gradient descent optimizer [19]. Multi-resolution registration was implemented to maximize efficiency [20, 21]. The registration process works most robustly when an approximate initializing transform is applied. This transform was generated through the alignment of at least three corresponding points on each image, although we could consider fully automated methods that use the centre of gravity to approximate the initial alignment of the images [22]. The selection of corresponding points was the only area of user-interaction required in our method. Once the initializing transform was determined, these points were no longer used in the remaining processing. B. Image Summation Once the images were registered, they were combined into what we define as a generalized shape image (GSI) as per the summation represented here: N ) V (i ) & GSI (i ) # " ' n $ n #1 ( N %
(1)
Subsequent to generating the GSI, an isosurface is chosen to represent the mean shape. We select the isosurface based on the histogram of an individual image, and then apply the same isosurface to all subsequent images. C. Image Summation The image gradient is defined as the change in the voxel intensity in each of the x, y or z directions, and the vector representing the image gradient is aligned in the direction of the greatest change in image intensity [23]. A small image
gradient occurs where there is a large shape variation present in the sample. This can be confirmed by the fact that in regions of the GSI where the image gradient is small, significantly different isosurfaces result from variations in the isovalue applied to the same GSI. Conversely, a large image gradient occurs where there is small shape variation and small isosurface variations result when different isovalues are applied to the same GSI. The image gradient was calculated by convolving the images with discrete difference masks to determine the direction of the image intensity gradient [24]. For the purposes of visualizing shape variation, it can be useful to apply the marching cubes algorithm [18] to extract an isosurface, and then probe the 3D image gradient data with that isosurface. The colours on the isosurface represent the gradient magnitudes (scalar values) corresponding to the spatial distribution of shape variation. The image gradient was derived through the calculation of central differences after the GSI has been Gaussian filtered (" = 1.2, support 1), and the probing of this dataset was performed by linear interpolation. D. Surface-to-Surface Distances The calculation of surface-to-surface distances can be used to identify differences in shape between two different sample groups – either between GSIs, or between individuals and a GSI. The surface-to-surface distance calculation is analogous to the concept of volume-based thickness measurements using maximal spheres designed to calculate trabecular thickness [25]. We adapted this concept to surface-based measurements to assess differences in shape by fitting spheres to calculate the closest-point distances between two surfaces. The surface-to-surface distance calculation requires that the two samples be superimposed. This can be performed using rigid image registration followed by selection of an appropriate isosurface value for each image. One image must be selected as the reference image, and the distances to an input image are displayed as scalar values on the isosurface of this reference image. The spheres used to calculate the closest point distances are then expanded outwards from the reference image’s surface until each sphere touches the nearest point of the input surface. The radii of these spheres are the Euclidean distances between the shapes, and represent the mean shape differences. These distances from the reference surface to the input are displayed spatially over the surface of the input image.
III. VALIDATION The technique of defining a GSI, visualization of the shape variation from the image gradient, and the Euclidean difference between shapes is demonstrated. Two datasets were used including (1) a set of known geometric shapes with a priori known shape variation, and (2) two sets of µCTmeasured mouse skulls from two different strains of mice commonly used in our laboratory.
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TMBE-00886-2006.R3 A. Geometric Shape Modified spheres were generated to assess the ability to accurately detect spatial shape variation. Eleven concentric spheres of radius 5.0mm were created, and a cylindrical appendage of length 7.5mm from the centre of the sphere and with varying radii (0.5mm to 1.5mm, in 0.1mm increments) was attached to the spheres. The modified spheres had a constant intensity of 1000 (CT number). A GSI of all eleven modified spheres was created, and the corresponding image gradient was calculated to determine the shape variation in the sample set. The modified spheres were also used to demonstrate the method’s sensitivity to registration. Surface-to-surface distances between a sphere (radius 5.0mm) and a modified sphere (spherical radius 5.0mm, cylindrical radius 1.0mm) were calculated to assess the accuracy of the surface-to-surface method. The reference image was chosen to be the sphere and the input image was the modified sphere. B. Biological Example: Mouse Skulls Twenty C57BL/6J and twenty A/WySnJ mouse skulls at age 90 days were analysed to demonstrate the applicability of the method to biological samples. Three-dimensional images of the skulls were acquired in vitro by !CT (35 !m isotropic resolution, vivaCT 40, Scanco Medical, Bassersdorf, Switzerland) using a standard mouse skull protocol [26]. Image resolution was decreased by a factor of two in each of three dimensions to facilitate analysis resulting in an isotropic resolution of 70 !m. Multi-resolution registration was performed as previously described, and a GSI for each strain was created from all twenty skulls in each sample set. A gradient operator was applied to determine the shape variation within each group of mice. Differences in shape between the two strains of mice were measured by applying the surface-tosurface distance measurement between the two groups. IV. SENSITIVITY ANALYSIS A. Filtration Testing the dependence of isosurface and gradient generation on the amount of filtration applied to the images, varying levels of Gaussian filtration were applied to the concentric sphere GSI. Both the filtration applied to the image and the filtration applied to the image gradient were varied. The three different levels of Gaussian filtration used were: zero (" = 0, support 0), moderate (" = 1.2, support 1), and large (" = 3, support 2). B. Registration The sensitivity of registration errors on the calculation of shape variation was investigated. A GSI of six modified spheres was created. Five of the shapes are modified spheres of varying cylindrical radii (0.8mm to 1.2mm in 0.1mm increments) while the sixth shape is a modified sphere of cylindrical radius 1.0mm rotated 90° about the z-axis. Rotating this shape by 90° is a simple means of simulating a failed registration by a lack of alignment in the cylindrical appendages.
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V. RESULTS An isovalue of 500 was used to visualize the mean shape of the modified sphere GSI (Fig.1a). The gray scale values of the 2D slice through the centre of the GSI illustrate that the shape variation is localized to the cylindrical region (Fig. 1b). The shape variation is presented as a colour map of the magnitude of the image gradient superimposed on the surface of the GSI (Fig. 1c). Again, the shape variation was confined to the cylindrical region of the modified sphere as expected. Surface-to-surface distances from a sphere (radius 5.0mm) to a modified sphere (spherical radius 5.0mm, cylindrical radius 1.0mm) were presented as a colour map superimposed on the surface of the modified sphere (Fig. 1d). The surface-tosurface distance was zero in the spherical region as expected because the sphere and the modified sphere had identical radii. The cylindrical region of the modified sphere was highlighted, and the surface-to-surface distance was a maximum magnitude of 2.5mm at the tip of the cylinder corresponding to the a priori known distance of 2.5mm from the sphere. This distance was shown as a negative because it is calculated from the surface of the modified sphere to the surface of the sphere. The mean shapes for both the A/WySnJ and C57BL/6J mouse skulls are presented (Fig. 2a,b). The variation between the twenty individuals comprising the mean was illustrated, where the magnitudes of the image gradients were superimposed on the surfaces of the mean mouse skulls (Fig. 2c,d). Two dimensional anterior-posterior slices through the A/WySnJ mouse skull GSI illustrate the areas of high shape variation (Fig. 2e). These areas are concentrated around the incisors of both strains and the lateral body of the mandible of the A/WySnJ strain. A surface-to-surface distance filter was applied to calculate the differences in shape between the A/WySnJ and C57BL/6J mouse skull mean images. The results are presented as a colour map superimposed on the surface of the C57BL/6J mean shape skull (Fig. 2f,g). The surface-to-surface gradient images demonstrate that the two strains have differently shaped cranium, premaxilla/maxilla region and squasmosal portion of the zygomatic arch. The gradient represented by the blue colour indicates regions where A/WySnJ mice are smaller than the C57BL/6J mice (absolute value of 0.5mm), while the green colour indicates regions where the skulls do not differ from each other in shape. The process is sensitive both to filtration and registration as demonstrated by the concentric sphere with varying amounts of image and gradient filtration (Fig. 3a). Increasing the image filtration smoothes the image, and increasing the gradient filtration alters the shape variation detected. The quantification of shape variation by our approach is also dependent on the registration process. A 2D slice through the centre of the mean shape modified sphere GSI highlights the large shape variation in the cylindrical region aligned along the x-axis (Fig. 3b). The misregistered shape produces a region of low image intensity, with a constant image gradient. This region appears as an area of shape variation when the gradient magnitudes are superimposed on the surface of the
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TMBE-00886-2006.R3 mean shape GSI (Fig. 3c). However, this region is identified as having a smaller amount of shape variation than the cylindrical region along the x-axis. VI. DISCUSSION The approach outlined here combines standard image processing methods in a unique combination to determine shape variation, as well as differences in shape between and within groups, and between individuals and the group mean. In addition to providing quantitative output, qualitative results are presented in an intuitive manner using well established visualization methodologies by superimposing gradient magnitudes on the 3D image surface.Qualitative results can provide insight into shape variation, and inclusion of the full 3D image for this purpose is an advantage compared to established GM techniques that display the results as wireframes or complicated matrices of numbers. This method is unique in that it displays the results directly on the 3D image of the specimen under analysis and requires little user interaction, and in contrast to voxel-based morphometry and other current methods, is novel in that it involves the generation of 3D average shapes and exploits the information included in these average shapes to calculate shape variation via image gradients. The approach is sensitive to filtration as demonstrated (Fig. 3a), primarily affecting how “smooth” the image appears and the spatial variation of image gradients. Zero filtration results in a gradient that fluctuates dramatically from voxel to voxel due to noise, but too much filtration removes shape variation across the surface. We found for our mouse data that applying Gaussian filtration to the image data (" = 1.2, support 1), and increased filtration for the gradient data (" = 3, support 2) worked well. Another important consideration is that the results are dependent on the success of the rigid image registration [15, 27, 28]. If mis-registration occurs, the image gradient analysis could indicate regions of high shape variation which are not biologically relevant. This process is illustrated with the use of modified spheres (Fig. 3b,c). The accuracy of registration of micro-CT has been established to be low (
