Accurate image alignment is essential for monitoring crack evolution in structural health monitoring (SHM), particularly under real-world conditions involving perspective distortion, occlusion, and low contrast. However, traditional feature detectors such as SIFT and SURF, which rely on Gaussian-based scale spaces, tend to suppress high-frequency edges, making them unsuitable for thin crack localization. Lightweight binary alternatives like ORB and BRISK, while computationally efficient, often suffer from poor keypoint repeatability on textured or shadowed surfaces. This study presents a physics-informed alignment framework that adapts the open KAZE architecture to SHM-specific challenges. By utilizing nonlinear anisotropic diffusion to construct a crack-preserving scale space, and integrating RANSAC-based homography estimation, the framework enables accurate geometric correction without the need for training, parameter tuning, or prior calibration. The method is validated on time-lapse images of masonry and concrete acquired via handheld smartphone under varied field conditions, including shadow interference, cropping, oblique viewing angles, and surface clutter. Compared to classical detectors, the proposed framework reduces crack area and spine length errors by up to 70 percent and 90 percent, respectively, while maintaining sub-5 percent alignment error in key metrics. Unsupervised, interpretable, and computationally lightweight, this approach supports scalable deployment via UAVs and mobile platforms. By tailoring nonlinear scale-space modeling to SHM image alignment, this work offers a robust and physically grounded alternative to conventional techniques for tracking real-world crack evolution.