Understanding the decisions of deep learning (DL) models is crucial for their acceptance in risk-sensitive applications. Class activation maps (CAMs) are commonly used in image analysis to visualize model reasoning by generating attention maps where signal intensities represent contributions to outputs. However, existing CAM algorithms focus on optimal weight design and salient feature layer selection, neglecting two key limitations in population-level interpretation: (1) lack of an appropriate intensity scale for proper interpretation and quantitative analysis, and (2) inability to identify which features within selected layers predominantly drive model reasoning. These gaps can lead to miscorrelations between CAMs and model outputs, causing erroneous interpretations, while restricting CAMs to case-specific visual inspections. We propose a framework to statistically analyze DL-extracted features at a population level, determinizing feature contributions for global intensity scaling and within-layer feature distinction. The global intensity scale standardizes CAMs, achieving high correlation coefficients (R) with model outputs. Within-layer feature distinction identifies overfitting, confounding factors, outliers, redundancies, and principal features. Applied to eight datasets, including five medical imaging datasets, this framework improved Rs between CAMs and outputs by 10.7–64.2%, achieving near 100% consistency. Furthermore, distinguishing principal features (5–25% in the selected layer) produced CAMs of equal quality while maintaining model output accuracy. This method, relying on minimal assumptions, enhances CAM-model consistency and broadens CAM applications by enabling standardized interpretation and deeper feature-level insights.

The intensity or gray-level derivatives have been widely used in image segmentation and enhancement. Conventional derivative filters often suffer from an undesired merging of adjacent objects because of their intrinsic usage of an inappropriately broad Gaussian kernel; as a result, neighboring structures cannot be properly resolved. To avoid this problem, we propose to replace the low-level Gaussian kernel with a bi-Gaussian function, which allows independent selection of scales in the foreground and background. By selecting a narrow neighborhood for the background with regard to the foreground, the proposed method will reduce interference from adjacent objects simultaneously preserving the ability of intraregion smoothing. Our idea is inspired by a comparative analysis of existing line filters, in which several traditional methods, including the vesselness, gradient flux, and medialness models, are integrated into a uniform framework. The comparison subsequently aids in understanding the principles of different filtering kernels, which is also a contribution of this paper. Based on some axiomatic scale-space assumptions, the full representation of our bi-Gaussian kernel is deduced. The popular γ-normalization scheme for multiscale integration is extended to the bi-Gaussian operators. Finally, combined with a parameter-free shape estimation scheme, a derivative filter is developed for the typical applications of curvilinear structure detection and vasculature image enhancement. It is verified in experiments using synthetic and real data that the proposed method outperforms several conventional filters in separating closely located objects and being robust to noise.