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The morphological characterization of quasi-planar structures represented by gray-scale images is challenging when object identification is sub-optimal due to registration artifacts. We propose two alternative procedures that enhances object identification in the integral-geometry morphological image analysis (MIA) framework. The first variant streamlines the framework by introducing an active contours segmentation process whose time step is recycled as a multi-scale parameter. In the second variant, we used the refined object identification produced in the first variant to perform the standard MIA with exact dilation radius as multi-scale parameter. Using this enhanced MIA we quantify the extent of vaso-obliteration in oxygen-induced retinopathic vascular growth, the preventative effect (by photobiomodulation) of exposure during tissue development to near-infrared light (NIR, 670 nm), and the lack of adverse effects due to exposure to NIR light.
© 2014 Optical Society of America
1. Introduction
The primary goal of morphological analysis is to quantify the relationship between geometrical aspects of complex structures and their physical properties which define their normal/abnormal state and function. This analysis often reveals insights of the (biological) mechanism leading to a particular structural form, provides a route to improve on (engineering) specifications for a designed structure, or establish a benchmark when analytical results for artificial models exist. Examples of such analysis vary from trabecular bone morphometry [1], fundamental biological processes leading to retinal morphology and branching [2], to the characterization of metal foams [3].
Integral-geometry morphological image analysis (MIA) is a general framework exploiting generalizations of the concept of area and volume—generalized volumes or additive functionals, to perform morphological characterization. In this framework an object, (𝒪) represented by a binary image, undergo a multi-scale process characterized by scale parameter r, while the value of 3 additive functionals {𝒲i=1···3(𝒪r)} are recorded. The rate of change of these functionals provides rich morphological signatures for further statistical analysis.
When an object is defined by a gray-scale image, a common choice is to use the gray-levels themselves as an scale parameter. While fast, this approach is restrictive in its application scope, being appropriate for some applications while performing poorly on others, e.g. when gray-levels account for depth via shading cues and may interfere with the object morphology. Whenever it is possible to obtain an effective object identification by a simple thresholding procedure, the scale parameter is often taken as the radius of an exact dilation process—the Euclidean distance transform [4]. This process preserves global shapes better than the morphological operators of dilation and erosion with truncated structuring elements, see [4–6]. An ordinary example of the utility of such a procedure is the ubiquitous fractal analysis, in which an object is dilated, and the rate of change in area/volume gives the fractal (space covering) dimension characterizing the object shape. Observing how all additive functionals changes, as the object shape is varied in a controlled fashion, produces a morphological signature that characterizes the object shape, its spatial neighborhood and the process instigating the change in its shape. This framework has been used to perform analysis, classification and inference in a range of applications from material sciences [7,8], physics of polymers and statistical physics [9–13], to quantitative morphological classification of neuronal cell types [14–16].
We show that the MIA framework can be simplified—while improving object identification, by using the Chan-Vese active contour method [17] both as a multi-scale process (locally akin to dilation) and as a segmentation method. The Chan-Vese segmentation produces a binary image at each time step, a necessary requirement for integration with MIA—for the estimation of these functionals at that step. Thus, the use of the Chan-Vese segmentation process in the MIA procedure, replacing threshold and exact dilation, produces a streamlined morphological signature. The main contribution of this paper is therefore an improved morphological image analysis method for gray scale images representing objects, particularly complex, difficult to identify and segment quasi-planar structures. A by-product of this contribution is to use the refined segmented image generated by the active contour method to perform standard MIA with the exact dilation as scale parameter—a more controlled multi-scale process which preserves object morphology for a longer range.
It has been recently hypothesized that if near infrared light (670nm) could protect against oxygen induced retinopathy (OIR), it would provide a preventative strategy for retinopathy of prematurity (ROP), for which it is a close model [18]. This implies that it is possible to reduce damage from exposure to oxygen and protect neuronal cells from damage. The protective effect of red light against OIR has been recently demonstrated by a combination of morphological and physiological methods, see [18]. To study these effects four groups of confocal microscope images (Zeiss, LSM-5) were established; images in group (A) are associated with retinas that only underwent exposure to near infrared light, images in group (B) are from retinas exposed to near-infrared (NIR) and displaying OIR, images in group (C) belong to retinas displaying oxygen induced retinopathy (OIR), and finally group (D), a matched control group. We apply both of the standard MIA procedures and our proposed adaptations to perform a morphological characterization of these vascular structures.
2. Methods
2.1. Oxygen induced retinopathy models
This work was conducted using Sprague-Dawley albino rats. All animal experimentation was conducted in accordance to the ARVO statement for the Use of Animals in Ophthalmic and Vision Research and with the approval of the Animal Ethics Committee at the Australian National University, Canberra (protocol-A2011/029). Animals were raised and experiments conducted in cyclic 5 lux light (12hrs:12hrs). All animals were culled using cervical dislocation. All culling was performed at 9am to control for possible circadian effects.
At birth (P0) pups and dam were placed in an Oxycycler (Biospherix Ltd., Lacona, NY) with 24 hours cyclic oxygen, 80% for 22 hours: 21% (normoxia) for 2 hours. Animals were maintained in this way till P18 where they were culled, and the eyes and organs harvested for further investigation. Animal weights and lengths were measured daily and records of animals deaths recorded.
2.2. 670nm red light treatment
Animals were exposed to 670nm red light only when damage was occurring. For the mouse model this was between P7-P17 and for the rodent model this was from P0 – P18. Animals were exposed to 670nm red light from a WARP 75 source (Quantum Devices Inc, Barneveld, WI, USA). Each animal was held approximately 2.5cm from the light source and treated to daily 3 minutes exposure to 670nm. This arrangement provided a fluence of 9J/cm2 at the eye. Animals were treated The animals did not appear agitated by the red light. All treatments were performed at 9am.
Treatment with 670nm red light have been shown to promote retinal healing [19] and modulates expression of genes related to inflammation, oxidative metabolism and apoptosis [20]. 670nm red light has also been shown to be a neuroprotectant against light induced damage [21, 22] and toxins [23]. There is evidence to suggest that cytochrome c oxidase (CCO) acts as the primary photo-acceptor/chromophore, boosting oxidative metabolism [24] and ATP production [25].
Previous work demonstrating evidence for the protective effects of the 670nm light have used a combination of physiological and morphological methods, see [18, 26] and references there in.
2.3. Retinal whole-mounts
Retinal whole-mounts were prepared using an established technique [27] with slight modifications. Briefly, eyes were removed and immediately fixed in 4% paraformaldehyde for 1 hour. Following fixation they eyes were rinsed 3 times in phosphate buffered saline (PBS) The retinas were removed from the eyecup, and placed under a dissection microscope (Leica, MZ16A).
To whole-mount the retina an ophthalmic surgical blade was used to create four incisions 1mm from the optic nerve head to the peripheral retina. Retinas were fixed in 4% paraformaldehyde for four hours then washed overnight in PBS. Retina were then washed with PBS for three intervals of 30 minutes and placed in a FITC conjugated lectin stain (Sigma, Missouri, USA; category number L2895) at a ratio of 1:100 with PBS for 24 hours, followed by rinsing with PBS for three intervals of 30 minutes. Retinas were then whole-mounted on slides and visualised using a confocal microscope (Zeiss, LSM 5). Assessment of the neovascularisation and vaso-obliteration was performed as a blinded assessment using an technique described previously in [27] Individual images were stitched together to create whole retinal images and prepared for publication using Adobe Photoshop CS4, however no modifications (gain or contrast adjustments) were performed.
3. Integral-geometry morphological image analysis (MIA and gMIA)
The MIA framework shares the same roots in mathematical morphology with another image analysis approach pioneered by Matheron [28], Serra [29, 30], and Soille [31] which is unfortunately referred to by the same acronym (MIA) in other research fields. The literature of both approaches has significant overlap. We use the term MIA here to refer throughout this paper unambiguously to the framework consolidated in the physics community, see for example [7,11,32]. A comprehensive source of the theory and the historical developments of integral and stochastic geometry can be found in [33].
Gray scale images in the MIA framework are usually transformed to a binary image by thresholding to an optimal gray-level. The active pixels of this image (the object) then undergo an exact dilation [4] process, and the change in the value of functionals Wν of the object at each dilation radius is recorded, producing a multi-scale morphological signature for that object. We refer to this approach using exact dilation with the acronym MIA in this paper. A simpler, often used alternative is to simply use all gray-levels as multi-scale indexes and calculate the additive functionals for each black and white image generated by thresholding to that level without dilation the object. We refer to this alternative procedure throughout this paper as gMIA.
These geometric measures, Wν, consist of all functionals of the image obeying the additive property, W (𝒪A ∪ 𝒪B)= W (𝒪A) + W (𝒪B) − W (𝒪A ∩ 𝒪B), and for this reason are called additive functionals. The area A of an object (the sum of its pixels) clearly satisfies this property. Less obviously, the perimeter P and the Euler Number χ–the number of connected components minus the number of holes, completes the set for 2D images. These quantities are therefore viewed as a generalization of the notion of the Area (Volume) of an object, and are also called generalized volumes or yet Minkowski functionals.
This methodology is a very powerful morphometric tool for when object identification is not critical, e.g. in clean, sharp, computer tomography images of man-made materials. We show in this paper that there is room for improving this method and to extend its use to often harder to identify biological forms.
4. MIA variants (sMIA and cMIA)
4.1. Enhanced object identification
We describe in this section the use of an iterative segmentation technique known as Active Contours or Snakes to improve object identification in MIA. This technique have as a common feature the minimization of a functional that controls the smoothness of a curve and its tendency to move towards to, and stop at, the boundaries of objects. See for example a recent application in CT image data for semi-automated segmentation [34] using the fast marching (FM) method [35, 36]. Some of these methods accept a formulation in terms of Level Sets, naturally detecting interior boundaries or holes.
Although a range of active contours methods could be employed in conjunction with MIA, we selected a method (Chan-Vese) first introduced in [17], as it modulates the same functionals of MIA and also provides a binary segmentation at each iteration step. The Chan-Vese segmentation also probes the neighborhood of the object at close range, providing a locally similar alternative to exact dilation, and retaining the multi-scale properties of the standard MIA.
We rely on the implementation of active contours in [17] using an objective function adapted from the Munford-Shah functional [37], but where the contours are attracted to the object border without the need to specify a gradient function. This objective function is given by
where u0(x, y) is an initial contour, c =(c1, c2) are the average value of u0(x, y) inside and outside Γ, μ and ν are non-negative penalties against the growth of the area A and perimeter P, while λ1 and λ2 are non-negative penalties against inside and outside fit, respectively. The curve Γ is found by solving the optimization problem The proof of the existence of minimizers for this problem is based on the fact that it is a particular case of the minimum partition problem, whose solution was proved in [37].4.2. Mezzotint (Halftoning) initialization
The ability of the human visual system to identify objects in face of several types of artifacts is extraordinary, and this subjective object identification is the litmus test for segmentation algorithms. Here we exploit a binarization mechanism to leverage this unmatched human performance in object identification. Since early days of printing techniques, the time-honoured binarization process of mezzotint (also known as halftoning or dithering) have been used and improved to appease human visual perception–the final arbiter. We used one traditional form of these techniques, halftoning by error-diffusing [38], as preprocessing stage to be used in conjunction with MIA. As per design, this initial binarization produces a very convincing segmentation from a distant viewpoint. From close inspection, all that is left disturbing the segmentation are short-range textured patches. Figure 1 illustrate how effective this process is, showing an example of a blood vessel confocal image in gray scale on the left, and in the middle a mezzotint, binary, version of the original. This mezzotint version of the original is used as the initial contour u0(x, y) in the Chan-Vese objective function, Eq. (1). At the right end of Fig. 1 we show the almost fully converged Chan-Vese segmentation of the original image at the far left.
Fig. 1 The flow chart of the sMIA procedure. A gray scale image of a retina exposed with near-infrared light (top middle), its mezzotint version (top left) and the final binary image (top right) produced from Chan-Vese active contour method at a time-step close to convergence.
The reliance on a preprocessing stage finely tuned to Human perception could be regarded here as an attempt to incorporate perceptual or structure vision clues to morphological image analysis. A second biomimetic aspect highlighted here is also a justification for the use of addictive functionals, beyond its proven computational effectiveness, in morphological analysis (MIA) and in the choice of the Chan-Vese objective function 1. Advances on the understanding of human perception of textures [39–41] and natural vision [42] single out specific combinations of higher order pixel correlations, as to what we perceive as salient in textures, and set natural images apart [42].
4.3. Streamlined MIA
As the Chan-Vese process proceeds towards a minimum of the functional in Eq. (1), a series of binary segmentations of the original image is produced. At some point (often in towards the end) in this process a best segmentation occurs, but clearly this perceptually best can be highly subjective.
One approach is to use the last image in the process, and perform the standard MIA procedure, we refer to this method here with the acronym cMIA. Alternatively we can create a morphological signature from this series of images that include this elusive best segmentation by recording the values of the additive functionals (A, P, χ) at every time-step. We refer to this streamlined procedure as sMIA.
5. Results
For each image three morphological signatures based on At, Pt and χt are produced. For the Chan-Vese segmentation process the scale parameter t refers to the time step of the process. For the standard MIA procedures (MIA and cMIA) the multi-scale parameter is given by the dilation radius t = r, and for gMIA the grayscale value is used, t =[0 – 255]. See examples of these profiles in Figs. 2, 3, 4, and 5.
The difference between MIA and cMIA in Fig. 2 and 5 is only on the starting point of the multi-scale process. MIA utilizes only a threshold value to binarize the initial image, then this image is dilated and the scale of this dilation is used as multi-scale parameters. On the other hand, cMIA utilizes the last point of the Chan-Vese segmentation, a visually improved binary version of the original image. This image is then dilated in the same way as MIA, so it is expected that the multi-scale signatures are similar.
An evident disadvantage of both cMIA and sMIA is that they are considerably slower than MIA and gMIA, as the exact dilation process is highly efficient. This can be an issue if images are too large and/or there are too many classes/samples. For the experiment reported here this was not an issue: sMIA takes approximately 8 seconds per image (200×200pixels) while MIA takes about one second, on a Xeon(R) W3690(3.47GHz) equipped computer.
By visual inspection of the original gray scale images there is a clear pattern of change in morphology. Its not possible to distinguish between group A (670 nm only) and group D (Control). While some samples of the group B (OIR+670 nm) may still display some of the extreme vaso-obliteration seen predominantly in group C (OIR only), most samples show significant recovery from retinopathy. This is attributable to spatial inhomogeneity of the effects of the 670 nm treatment and to the fact that we labeled sub-sampled images from all four retinal quadrants by the whole retina treatment label, irrespective of the extent of their treatment effect.
In order to avoid the obvious morphological effect of oxygen induced retinopathy in the periphery of the retina (see Fig. 6), we manually crop a large region of each quadrant, containing at least 4 levels of branching for each treatment. This large image is then sub-sampled 50 times at random offsets for bootstrap. The data set therefore contains 200 images (four retina images per group) for each treatment group.
We quantify the morphological differences in branching in a supervised classification scheme, using the lower order fourier coefficients of the multi-scale signatures described above as feature vectors. We perform a 10-fold cross-validated quadratic discriminant analysis, which was the better fit for all four MIA variants. Table 1 shows the confusion matrix for this classification for each of the variants. The result is a very reliable classification for all methods, consistent with visual inspection, albeit with better classification recall, in this particular application, for sMIA and gMIA.
Table 1. Cross-validated confusion matrices between treatment groups for each variant of MIA.
The stability of the Euler number across scales seems to play a role in the slight better performance of sMIA (see Table 1) compared with the standard approach of MIA and gMIA, which can oscilate significantly at smaller scales. Nevertheless, the area functional is a fairly stable measure for all MIA variants (see Figs. 2, 3, 4, and 5), so it seems that the perimeter and Euler number, which are more stable in the sMIA procedure, helps improve classification in the current study.
We illustrate the relationship between treatments using a form of agglomerative hierarchical clustering. Starting with each sample as a cluster of its own, in each step clusters are then combined into larger clusters, until a predetermined number of clusters is achieved. At each step, the two clusters separated by the shortest distance (we use the Mahalanobis distance) are merged. In single-linkage [43], the link between two clusters is made by those two elements (one in each cluster) that are closest to each other. Figure 7 displays a hierarchical clustering of the four treatment of the retina, showing the trace of cluster merging and the distance at which each merging occurred.
Fig. 7 Hierarchical clustering dendrogram of treatments samples from cross-validated confusion matrix for each MIA variant technique: standard MIA (MIA), streamlined MIA (sMIA), MIA initiated with a Chan-Vese segmentation (cMIA) and with a grayscale mia (gMIA). The treatment groups are: A (670 nm only), group B (OIR+670 nm), group C (OIR only), and group D (Control).
While consistent with our prior knowledge of the true labelling, the MIA variants attribute varying levels of similarity between groups. Notably for sMIA, group A (670 nm only) and group D (Control) are all but indistinguishable, while the similarity of group B (OIR+670 nm), group C (OIR only) are for gMIA.
The classification performance of the MIA variations is indicative of the potential for morphological analysis, not a final word on the merits of each method. In a more complex morphological classification, one could use the features of all four variant methods and select the best ones using a principled feature selection technique such as the lasso, ridge regression or a combination of both in the elastic net [44].
6. Discussion
6.1. Quantification of retinopathy
Although a range of metrics could also be used in quantitative morphometry, we argue that the additive functionals are the natural first step, and often sufficient. These measures by themselves are rotationally invariant, have a mixture of metric and topological features and are the only additive measures of planar images (any other additive and invariant measure must be a combination of these). Furthermore, the multi-scale treatment of these measures, being it through exact dilation or the proposed Chan-Vese procedures, enables a refined quantitative analysis of biochemical, physical and transport processes that might affect the morphology in subtle ways which are difficult to identify by visual inspection alone. Being the nature of the retinal vasculature fractal itself and, the space covering dimension directly related to multi-scale area, one would naturally expect that any departure from normality might affect the fractality of such structure, which would be captured by changes in the slope of the area functional and the other morphological signatures.
6.2. Image artifacts
Artifacts that obscure object identification will affect morphological and morphometric analysis. Therefore during image acquisition one must insure proper focus and minimal reflections. The geometric measures we calculate must be closely related to the object whose morphology we want to quantify. Of the three additive functionals the one more critically affected by artifacts is the Euler Number. Nevertheless, by performing the morphological analysis in a multi-scale fashion (exact dilation) some artifacts, such as noise, is averaged out. The Chan-Vese process is robust against disconnected strong reflections, as reflections are circular they would tend grow at maximum rate (distinct to the body of the object which is fractal) and be penalised for it.
6.3. Statistics
The statistical analysis for consistency of the treatments effects and significance of group membership elicited by sMIA was done in a prior study published recently [18]. In the current work the focus is on comparing sMIA with its alternatives, and for that we used bootstrapping. In other words the source of variability in our experiment comes from the different lobes (quadrants) and the sub-samples within each lobe: i) Each animal produces four lobes with similar but visually distinct morphologies as the effect of treatment is not homogeneous. ii) We also spatially sub-sampled each lobe, adding (bootstrap) further to the variability of the image samples. Overcoming this variability is the task that all 4 variants of MIA should face and are tested by their classification performance.
7. Conclusion
In this paper we presented two alternatives procedures for the morphological image analysis of gray scale images. An streamlined version of MIA is created by recording the values of Minkowski functionals throughout the Chan-Vese active contour method initialized with mezzotint version of the original gray scale image, producing a multi-scale morphological signature. Alternatively we performed the usual exact dilation of the last image in the Chan-Vese process, a significant improvement on segmentation by threshold binarization.
We applied this approach to the characterization of images representing the vessels of the retinas subjected to three different treatments and a control group. A clear and consistent pattern of morphological changes emerged across all methods considered: the sMIA method introduced in this paper and the standard MIA method with 3 different initializations. This pattern is consistent, albeit with varying levels of resolution and efficiency, with the recent findings of the beneficial effects of near-infrared (NIR) as preventative of oxygen-induced retinopathy (OIR) which is an important proxy model for retinopathy of prematurity (ROP), see [18].
The results of the morphological analysis presented here are therefore encouraging, given the known artifacts (visible) in the data set and given that the morphological effects of the treatments are non-uniform across the four retinal quadrants. Even in presence of these artifacts, integral-geometry morphological analysis can be a quick and effective tool to formulate and validate hypothesis relating to and exploring biological form and function. The enhanced object identification described in this paper might be of value also outside the realm of MIA, e.g. for subsequent comparative morphological analysis, such as the Sholl branching analysis [2].
Acknowledgments
This work was supported by Grant CE0561903 from the Australian Research Council through the ARC Centre of Excellence in Vision Science.
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