Perception-based visualization of manifold-valued medical images using distance-preserving dimensionality reduction

Dimensionality Reduction and Electrode Arrangement Optimization for an Electric Field Source Seeking Surgical Navigation Method

This study proposes a Dimensionality Reduction Electric Field Source Seeking (EFSS) method for real-time, high-precision navigation in intracranial puncture surgeries. The method integrates internal localization electrodes and external potential measurement electrodes to minimize surgical trauma while ensuring the accurate localization and guidance of surgical instruments. To optimize the electrode arrangement, two evaluation metrics-Mean Response Coefficient (MRC) and MRC-mean-were introduced. The simulation results demonstrated the effectiveness of these metrics, with the optimal arrangement achieving an average localization error below 2 mm and a 56% reduction in error after optimization. Experimental validation was conducted using a brain model with conductivity properties similar to those of human tissue. Localization experiments confirmed the robustness and accuracy of the EFSS method, with all results showing consistent repeatability and monotonic trends in performance across different electrode configurations. This study highlights the potential of the dimensionality reduction EFSS method as a novel and effective approach for navigation in minimally invasive intracranial surgeries.

Method for Adapting the Grayscale Standard Display Function to the Aging Eye

Perceptual linearity of grayscale images based on a contrast sensitivity model is a widely recognized and used standard for medical imaging visualization. This approach ensures consistency across devices and provides perception of luminance variations in direct relationship to changes in image values. We analyze the effect of aging of the human eye on the precept of linearity and demonstrate that not only the number of just-noticeable differences diminishes for older subjects but also linearity across the range of luminance values is significantly affected. While loss of JNDs is inevitable for a fixed luminance range, our findings suggest possible corrective approaches for maintaining linearity.

Visualizing Tensor Normal Distributions at Multiple Levels of Detail

Despite the widely recognized importance of symmetric second order tensor fields in medicine and engineering, the visualization of data uncertainty in tensor fields is still in its infancy. A recently proposed tensorial normal distribution, involving a fourth order covariance tensor, provides a mathematical description of how different aspects of the tensor field, such as trace, anisotropy, or orientation, vary and covary at each point. However, this wealth of information is far too rich for a human analyst to take in at a single glance, and no suitable visualization tools are available. We propose a novel approach that facilitates visual analysis of tensor covariance at multiple levels of detail. We start with a visual abstraction that uses slice views and direct volume rendering to indicate large-scale changes in the covariance structure, and locations with high overall variance. We then provide tools for interactive exploration, making it possible to drill down into different types of variability, such as in shape or orientation. Finally, we allow the analyst to focus on specific locations of the field, and provide tensor glyph animations and overlays that intuitively depict confidence intervals at those points. Our system is demonstrated by investigating the effects of measurement noise on diffusion tensor MRI, and by analyzing two ensembles of stress tensor fields from solid mechanics.

Spectral edge: gradient-preserving spectral mapping for image fusion

This paper describes a novel approach to image fusion for color display. Our goal is to generate an output image whose gradient matches that of the input as closely as possible. We achieve this using a constrained contrast mapping paradigm in the gradient domain, where the structure tensor of a high-dimensional gradient representation is mapped exactly to that of a low-dimensional gradient field which is then reintegrated to form an output. Constraints on output colors are provided by an initial RGB rendering. Initially, we motivate our solution with a simple "ansatz" (educated guess) for projecting higher-D contrast onto color gradients, which we expand to a more rigorous theorem to incorporate color constraints. The solution to these constrained optimizations is closed-form, allowing for simple and hence fast and efficient algorithms. The approach can map any N-D image data to any M-D output and can be used in a variety of applications using the same basic algorithm. In this paper, we focus on the problem of mapping N-D inputs to 3D color outputs. We present results in five applications: hyperspectral remote sensing, fusion of color and near-infrared or clear-filter images, multilighting imaging, dark flash, and color visualization of magnetic resonance imaging diffusion-tensor imaging.

A high throughput and efficient visualization method for diffusion tensor imaging of human brain white matter employing diffusion-map space

Diffusion tensor imaging (DTI) possesses high dimension and complex structure, so that detecting available pattern information and its analysis based on conventional linear statistics and classification methods become inefficient. In order to facilitate classification, segmentation, compression or visualization of the data, dimension reduction is far-reaching. There have been many approaches proposed for this purpose, which mostly rely on complex low dimensional manifold embedding of the high-dimensional space. Dimension reduction is commonly applicable through linear algorithms, such as principal component analysis and multi-dimensional scaling; however, they are not able to deal with complex and high dimensional data. In this light, nonlinear algorithms with the capability to preserve the distance of high dimensional data have been developed. The purpose of this paper is to propose a new method for meaningful visualization of brain white matter using diffusion tensor data to map the 6-dimensional tensor to a three dimensional space employing Markov random walk and diffusion distance algorithms, leading to a new distance-preserving map for the DTI data with lower dimension and higher throughput information.

Spectral embedding based active contour (SEAC) for lesion segmentation on breast dynamic contrast enhanced magnetic resonance imaging

PURPOSE

Segmentation of breast lesions on dynamic contrast enhanced (DCE) magnetic resonance imaging (MRI) is the first step in lesion diagnosis in a computer-aided diagnosis framework. Because manual segmentation of such lesions is both time consuming and highly susceptible to human error and issues of reproducibility, an automated lesion segmentation method is highly desirable. Traditional automated image segmentation methods such as boundary-based active contour (AC) models require a strong gradient at the lesion boundary. Even when region-based terms are introduced to an AC model, grayscale image intensities often do not allow for clear definition of foreground and background region statistics. Thus, there is a need to find alternative image representations that might provide (1) strong gradients at the margin of the object of interest (OOI); and (2) larger separation between intensity distributions and region statistics for the foreground and background, which are necessary to halt evolution of the AC model upon reaching the border of the OOI.

METHODS

In this paper, the authors introduce a spectral embedding (SE) based AC (SEAC) for lesion segmentation on breast DCE-MRI. SE, a nonlinear dimensionality reduction scheme, is applied to the DCE time series in a voxelwise fashion to reduce several time point images to a single parametric image where every voxel is characterized by the three dominant eigenvectors. This parametric eigenvector image (PrEIm) representation allows for better capture of image region statistics and stronger gradients for use with a hybrid AC model, which is driven by both boundary and region information. They compare SEAC to ACs that employ fuzzy c-means (FCM) and principal component analysis (PCA) as alternative image representations. Segmentation performance was evaluated by boundary and region metrics as well as comparing lesion classification using morphological features from SEAC, PCA+AC, and FCM+AC.

RESULTS

On a cohort of 50 breast DCE-MRI studies, PrEIm yielded overall better region and boundary-based statistics compared to the original DCE-MR image, FCM, and PCA based image representations. Additionally, SEAC outperformed a hybrid AC applied to both PCA and FCM image representations. Mean dice similarity coefficient (DSC) for SEAC was significantly better (DSC = 0.74 ± 0.21) than FCM+AC (DSC = 0.50 ± 0.32) and similar to PCA+AC (DSC = 0.73 ± 0.22). Boundary-based metrics of mean absolute difference and Hausdorff distance followed the same trends. Of the automated segmentation methods, breast lesion classification based on morphologic features derived from SEAC segmentation using a support vector machine classifier also performed better (AUC = 0.67 ± 0.05; p < 0.05) than FCM+AC (AUC = 0.50 ± 0.07), and PCA+AC (AUC = 0.49 ± 0.07).

CONCLUSIONS

In this work, we presented SEAC, an accurate, general purpose AC segmentation tool that could be applied to any imaging domain that employs time series data. SE allows for projection of time series data into a PrEIm representation so that every voxel is characterized by the dominant eigenvectors, capturing the global and local time-intensity curve similarities in the data. This PrEIm allows for the calculation of strong tensor gradients and better region statistics than the original image intensities or alternative image representations such as PCA and FCM. The PrEIm also allows for building a more accurate hybrid AC scheme.

Representation of lesion similarity by use of multidimensional scaling for breast masses on mammograms

Presentation of similar reference images can be useful for diagnosis of new lesions. A similarity map which can visually present the overview of the relationship between the lesions with different types may provide the supplemental information to the reference images. A new method for constructing the similarity map by multidimensional scaling (MDS) for breast masses on mammograms was investigated. Nine pathologic types were included; three regions of interests each from the nine groups were employed in this study. Subjective similarity ratings by expert readers were obtained for all possible 351 pairs of masses. Using the average ratings, MDS similarity map was created. Each axis of the MDS configuration was fitted by the linear model with 13 image features to reconstruct the similarity map. Dissimilarity based on the distance in the reconstructed space was determined and compared with the subjective rating. The MDS map consistently represented the similarity between cysts and fibroadenomas, invasive lobular carcinomas and scirrhous carcinomas, and ductal carcinomas in situ, solid-tubular carcinomas, and papillotubular carcinomas with the experts' data. The correlation between the average subjective ratings and the dissimilarities based on the distance in the reconstructed feature space was much greater (-0.87) than that of the dissimilarities based on the distance in the conventional feature space (-0.65). The new similarity map by MDS can be useful for visualizing the relationship between breast masses with different pathologic types. It has potential usefulness in selecting the similarity measures and providing the supplemental information.

Comparative analysis of nonlinear dimensionality reduction techniques for breast MRI segmentation

PURPOSE

Visualization of anatomical structures using radiological imaging methods is an important tool in medicine to differentiate normal from pathological tissue and can generate large amounts of data for a radiologist to read. Integrating these large data sets is difficult and time-consuming. A new approach uses both supervised and unsupervised advanced machine learning techniques to visualize and segment radiological data. This study describes the application of a novel hybrid scheme, based on combining wavelet transform and nonlinear dimensionality reduction (NLDR) methods, to breast magnetic resonance imaging (MRI) data using three well-established NLDR techniques, namely, ISOMAP, local linear embedding (LLE), and diffusion maps (DfM), to perform a comparative performance analysis.

METHODS

Twenty-five breast lesion subjects were scanned using a 3T scanner. MRI sequences used were T1-weighted, T2-weighted, diffusion-weighted imaging (DWI), and dynamic contrast-enhanced (DCE) imaging. The hybrid scheme consisted of two steps: preprocessing and postprocessing of the data. The preprocessing step was applied for B(1) inhomogeneity correction, image registration, and wavelet-based image compression to match and denoise the data. In the postprocessing step, MRI parameters were considered data dimensions and the NLDR-based hybrid approach was applied to integrate the MRI parameters into a single image, termed the embedded image. This was achieved by mapping all pixel intensities from the higher dimension to a lower dimensional (embedded) space. For validation, the authors compared the hybrid NLDR with linear methods of principal component analysis (PCA) and multidimensional scaling (MDS) using synthetic data. For the clinical application, the authors used breast MRI data, comparison was performed using the postcontrast DCE MRI image and evaluating the congruence of the segmented lesions.

RESULTS

The NLDR-based hybrid approach was able to define and segment both synthetic and clinical data. In the synthetic data, the authors demonstrated the performance of the NLDR method compared with conventional linear DR methods. The NLDR approach enabled successful segmentation of the structures, whereas, in most cases, PCA and MDS failed. The NLDR approach was able to segment different breast tissue types with a high accuracy and the embedded image of the breast MRI data demonstrated fuzzy boundaries between the different types of breast tissue, i.e., fatty, glandular, and tissue with lesions (>86%).

CONCLUSIONS

The proposed hybrid NLDR methods were able to segment clinical breast data with a high accuracy and construct an embedded image that visualized the contribution of different radiological parameters.