Topological Characterization of Signal in Brain Images Using Min-Max Diagrams

Abstract

Abstract. We present a novel computational framework for characterizing signal in brain images via nonlinear pairing of critical values of the signal. Among the astronomically large number of different pairings possible, we show that representations derived from specific pairing schemes provide concise representations of the image. This procedure yields a "min-max diagram" of the image data. The representation turns out to be especially powerful in discriminating image scans obtained from different clinical populations, and directly opens the door to applications in a variety of learning and inference problems in biomedical imaging. It is noticed that this strategy significantly departs from the standard image analysis paradigm -where the 'mean' signal is used to characterize an ensemble of images. This offers robustness to noise in subsequent statistical analyses, for example; however, the attenuation of the signal content due to averaging makes it rather difficult to identify subtle variations. The proposed topologically oriented method seeks to address these limitations by characterizing and encoding topological features or attributes of the image. As an application, we have used this method to characterize cortical thickness measures along brain surfaces in classifying autistic subjects. Our promising experimental results provide evidence of the power of this representation.

Evaluating dementia risk from MRI by fuzzy inference model

“…From the spherical brain image we reconstruct the distribution of the cortical thickness in order to map it in a 2D plane. Finally, the min-max diagram method [5] is used to match the homology of cortical thickness and plot its topological characteristics. To verify the feasibility of our proposed model, we use MRI examinations from normal and suspected AD to obtain the topological characteristics and their distributions.…”

“…The study pointed out that, indeed, the variation of cortical thickness and AD are highly correlated. A second study by Chung et al [4] [5] used MRI (Magnet Resonance Imaging) examinations and signal processing afterwards to extract and set up the brain cortical thickness and its characteristics distribution.…”

Sparse topological data recovery in medical images

“…The main tool for investigating the topological change of the excursion set is persistent homology [14,15,16]. Using Morse theory, we can determine the topological The simplicial complex of the underlying topology of critical values can be constructed using the Delaunay triangulation [18]. deformation of the excursion sets by tabulating the occurrence of critical values [14].…”

“…deformation of the excursion sets by tabulating the occurrence of critical values [14]. This framework is general enough for dealing with a wide variety of noisy multivariate data including brain images [17,18], networks [19,20] and gene expression [21].…”

“…Figure 1 shows an example of approximating 2D functional signal (cortical thickness) using the Delaunay triangulation [18]. The Delaunay triangulation is constructed on the extreme values of the signal.…”