Gaussian Function Model for Task-Specific Evaluation in Medical Imaging: A Theoretical Investigation

In medical image diagnosis, understanding image characteristics is crucial for selecting and optimizing imaging systems and advancing their development. Objective image quality assessments, based on specific diagnostic tasks, have become a standard in medical image analysis, bridging the gap between experimental observations and clinical applications. However, conventional task-based assessments often rely on ideal observer models that assume target signals have circular shapes with well-defined edges. This simplification rarely reflects the true complexity of lesion morphology, where edges exhibit variability. This study proposes a more practical approach by employing a Gaussian distribution to represent target signal shapes. This study explicitly derives the task function for Gaussian signals and evaluates the detectability index through simulations based on head computed tomography (CT) images with low-contrast lesions. Detectability indices were calculated for both circular and Gaussian signals using non-prewhitening and Hotelling observer models. The results demonstrate that Gaussian signals consistently exhibit lower detectability indices compared to circular signals, with differences becoming more pronounced for larger signal sizes. Simulated images closely resembling actual CT images confirm the validity of these calculations. These findings quantitatively clarify the influence of signal shape on detection performance, highlighting the limitations of conventional circular models. Thus, it provides a theoretical framework for task-based assessments in medical imaging, offering improved accuracy and clinical relevance for future advancements in the field.