Spatial Methods for Imaging Data

Spatial proteomics reveals immune cell organization, offering key insights into immune function and disease mechanism. Standard approaches assessing colocalization between cell types assume spatial homogeneity across samples. In real tissues, however, cell density patterns can vary substantially from patient to patient; if this heterogeneity is not incorporated, the resulting inference can be biased.
We propose a permutation-based, multi-scale test built on the Ripley's K function. For each sample and target cell-type pair, we compute Kcross curve over distances r (neighborhood radii) and average across samples to obtain an observed group-level curve. To preserve patient heterogeneity, we permute all cell-type labels within each sample. Each permutation yields one group-level permuted curve (averaged across samples); the set of permuted curves forms the empirical null for the group-level curve. We compute permutation p-values at each r by comparing observed curve to the null, then use the Cauchy combination test for a single global p-value. The procedure controls Type I error in both homogeneous and heterogeneous simulations, and identifies meaningful colocalization in TNBC tissue 

Shapes of objects in images are often complex, high-dimensional, and vary in ways not captured by standard Euclidean geometry and statistics. Statistical shape analysis encompasses methods with flexible and interpretable measures of the intrinsic shape and variability of shape in geometric objects. One such
method called Elastic Shape Analysis (ESA) measures differences in the shape of two objects invariant to transformations, such as rotation, scale, translation, and parameterization. While useful for many image applications, formal statistical inference methods applying ESA to an image are limited. In this paper we introduce a hypothesis testing method that computes empirical confidence intervals of the elastic shape distance (ESD) between the true shape and the estimated shape. This methodology enables testing whether a prespecified null shape of the latent structure could plausibly have generated the empirical data distribution. The effectiveness of the method is illustrated through several numerical studies and real world image examples in inertial confinement fusion (ICF). 

Measures of agreement have been extensively studied over the past three decades from multiple perspectives, reflecting both the objectives of specific studies and the nature of the data under analysis. For continuous data, beginning with the seminal concordance correlation coefficient introduced by Lin (1989), a wide range of extensions and modified coefficients has been proposed in the literature. Within the framework of spatial statistics, agreement measures have been further developed to assess concordance between two random fields. In this talk, we review recent methodological advances for agreement assessment in both geostatistical and lattice data settings. The proposed methodology is illustrated through two applications: forest data and the analysis of poverty rates in the Metropolitan and Valparaíso regions of Chile. These applications demonstrate the practical implementation of the approaches and highlight their main advantages and limitations. 

Sparse learning is a central topic in modern statistics, yet many widely used methods rely on assumptions that ignore measurement error and structural dependence in high-dimensional signals. Motivated by these limitations, we propose the CoCo–Fused Lasso, a structured sparse learning method that combines the convex correction framework of CoCoLasso with the fused Lasso penalty. Building on the work of Datta and Zou, the proposed approach addresses error-in-variables while simultaneously enforcing sparsity and piecewise-constant structure in the estimated parameters. This extension broadens the scope of sparse regression methods to settings where both measurement error and structured signals are present. The proposed estimator is formulated through a convex optimization problem and is computationally tractable. Simulation studies demonstrate improved estimation behavior relative to existing sparse estimators when structured signals are present. An application to denoising tomographic images of gold nanoparticles illustrates the practical benefits of the proposed method. 

Hierarchical multiplex imaging approaches generate spatially resolved single-cell measurements across multiple, spatially organized fields of view (FOVs) within patient tumor specimens, thereby enabling systematic investigation of how the organization of the tumor microenvironment varies along biologically meaningful intratumoral gradients. Existing approaches fail to jointly address this multi-resolution data structure needed to recover true biological signals. We propose MoSAIC: multi-resolution spatial regression analysis of cell colocalizations, a hierarchical Bayesian spatial regression model designed for multi-resolution spatial data. MoSAIC decomposes the joint variation into three model components: (i) global tumor-gradient effects, (ii) patient-specific effects to capture inter-patient variability, and (iii) Gaussian process models to account for spatial dependence between FOVs within each patient tumor tissue. Simulations demonstrate MoSAIC has improved prediction and model fit compared to existing spatial and non-spatial model alternatives. Our method is motivated by and applied to a renal cell carcinoma multiplex imaging cohort to investigate immune–tumor colocalization patterns across the epithelial-to-mesenchymal transition (EMT) gradient. MoSAIC identifies increased macrophage–tumor colocalization and decreased cytotoxic T–tumor colocalization progressing across the increasing EMT gradient, consistent with EMT-associated immune suppression and spatially varying immune engagement. Overall, MoSAIC provides an interpretable, multi-resolution framework for quantifying spatial tumor-gradient effects in cancer imaging studies. 

High-resolution imaging and other spatial biomedical measurements are naturally represented as tensors with ultrahigh-dimemsional correlated features, where sample sizes are modest and signals can be weak and spatially diffuse. We propose a fast, model-agnostic screening framework that ranks voxel- or region-level features by a kernel-based measure of outcome association, then improves stability and interpretability by smoothing the resulting importance map with anatomy-aware spatial regularization. The method is designed to preserve tensor structure by returning connected, axis-aligned subtensors. To address the common failure mode of purely marginal screening, we introduce a two-stage sufficient refinement. The first stage selects a small set of strong signals; the second stage evaluates remaining candidates conditionally on the first-stage set using low-rank summaries to keep computation scalable, with adaptive smoothing applied outside the initial selection. Simulation studies and brain imaging data show improved recovery of weak, spatially structured signals and more reproducible selected regions compared with marginal screening alone.