We consider the problem of characterizing shape populations using highly frequent representative shapes. Framing such shapes as statistical modes – shapes that correspond to (significant) local maxima of the underlying pdfs – we develop a frequency-based, nonparametric approach for estimating sample modes. Using an elastic shape metric, we define ϵ-neighborhoods in the shape space and shortlist shapes that are central and have the most neighbors. A critical issue – How to automatically select the threshold ϵ? – is resolved using a combination of ANOVA and empirical mode distribution. The resulting modal set, in turn, helps characterize the shape population and performs better than the traditional cluster means. We demonstrate this framework using amoeba shapes from brightfield microscopy images and highlight its advantages over existing ideas.
more »
« less
Radiologic Image-Based Statistical Shape Analysis of Brain Tumours
We propose a curve-based Riemannian geometric approach for general shape-based statistical analyses of tumours obtained from radiologic images. A key component of the framework is a suitable metric that enables comparisons of tumour shapes, provides tools for computing descriptive statistics and implementing principal component analysis on the space of tumour shapes and allows for a rich class of continuous deformations of a tumour shape. The utility of the framework is illustrated through specific statistical tasks on a data set of radiologic images of patients diagnosed with glioblastoma multiforme, a malignant brain tumour with poor prognosis. In particular, our analysis discovers two patient clusters with very different survival, subtype and genomic characteristics. Furthermore, it is demonstrated that adding tumour shape information to survival models containing clinical and genomic variables results in a significant increase in predictive power.
more » « less- NSF-PAR ID:
- 10398887
- Publisher / Repository:
- Oxford University Press
- Date Published:
- Journal Name:
- Journal of the Royal Statistical Society Series C: Applied Statistics
- Volume:
- 67
- Issue:
- 5
- ISSN:
- 0035-9254
- Page Range / eLocation ID:
- p. 1357-1378
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
more » « less
Abstract Many biomedical studies have identified important imaging biomarkers that are associated with both repeated clinical measures and a survival outcome. The functional joint model (FJM) framework, proposed by Li and Luo in 2017, investigates the association between repeated clinical measures and survival data, while adjusting for both high‐dimensional images and low‐dimensional covariates based on the functional principal component analysis (FPCA). In this paper, we propose a novel algorithm for the estimation of FJM based on the functional partial least squares (FPLS). Our numerical studies demonstrate that, compared to FPCA, the proposed FPLS algorithm can yield more accurate and robust estimation and prediction performance in many important scenarios. We apply the proposed FPLS algorithm to a neuroimaging study. Data used in preparation of this article were obtained from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database.
-
more » « less
Abstract Proliferation of high‐resolution imaging data in recent years has led to substantial improvements in the two popular approaches for analyzing shapes of data objects based on landmarks and/or continuous curves. We provide an expository account of elastic shape analysis of parametric planar curves representing shapes of two‐dimensional (2D) objects by discussing its differences, and its commonalities, to the landmark‐based approach. Particular attention is accorded to the role of reparameterization of a curve, which in addition to rotation, scaling and translation, represents an important shape‐preserving transformation of a curve. The transition to the curve‐based approach moves the mathematical setting of shape analysis from finite‐dimensional non‐Euclidean spaces to infinite‐dimensional ones. We discuss some of the challenges associated with the infinite‐dimensionality of the shape space, and illustrate the use of geometry‐based methods in the computation of intrinsic statistical summaries and in the definition of statistical models on a 2D imaging dataset consisting of mouse vertebrae. We conclude with an overview of the current state‐of‐the‐art in the field.
This article is categorized under:
Image and Spatial Data < Data: Types and Structure
Computational Mathematics < Applications of Computational Statistics
-
This work discusses new methodologies for identifying the grain boundaries in color images of metallic microstructures and the quantification of their grain topology. Grain boundaries have a large impact on the macro-scale material properties. Particularly, this work employs the experimental microstructure data of Titanium-Aluminum alloys, which can be used for various aerospace components owing to their outstanding mechanical performance in elevated temperatures. The grain topology of these metallic microstructures is quantified using the concept of shape moment invariants. In order to capture the grains using the shape moment invariants, it is necessary to identify the grain boundaries and separate them from their respective grains. We present two methodologies to detect the grain boundaries. The first method is the tolerance-based neighbor analysis. The second method focuses on creating three-dimensional space of pixel intensity values based on the three color channels and measuring the Euclidean distance to separate different grains. Additionally, since the grain boundaries may not possess the same material properties as the grain itself, this work investigates the effect of including the grain boundaries when determining the homogenized material properties of the given microstructure. To generate adequate statistical information, microstructures are reconstructed from the experimental data using the Markov Random Field (MRF) method. Upon separating the grains, we use the shape moment invariants to quantify the shapes of different grains. Using the shape moment invariants and the experimental material property values, three neural network functions are developed to investigate the effects of grain boundaries on material property predictions.more » « less
-
more » « less
Abstract IRF family genes have been shown to be crucial in tumorigenesis and tumour immunity. However, information about the role of IRF in the systematic assessment of pan‐cancer and in predicting the efficacy of tumour therapy is still unknown. In this work, we performed a systematic analysis of IRF family genes in 33 tumour samples, including expression profiles, genomics and clinical characteristics. We then applied Single‐Sample Gene‐Set Enrichment Analysis (ssGSEA) to calculate IRF‐scores and analysed the impact of IRF‐scores on tumour progression, immune infiltration and treatment efficacy. Our results showed that genomic alterations, including SNPs, CNVs and DNA methylation, can lead to dysregulation of IRFs expression in tumours and participate in regulating multiple tumorigenesis. IRF‐score expression differed significantly between 12 normal and tumour samples and the impact on tumour prognosis and immune infiltration depended on tumour type. IRF expression was correlated to drug sensitivity and to the expression of immune checkpoints and immune cell infiltration, suggesting that dysregulation of IRF family expression may be a critical factor affecting tumour drug response. Our study comprehensively characterizes the genomic and clinical profile of IRFs in pan‐cancer and highlights their reliability and potential value as predictive markers of oncology drug efficacy. This may provide new ideas for future personalized oncology treatment.
