Medical image registration is crucial for various clinical and research applications including disease diagnosis or treatment planning which require alignment of images from different modalities, time points, or subjects. Traditional registration techniques often struggle with challenges such as contrast differences, spatial distortions, and modality-specific variations. To address these limitations, we propose a method that integrates learnable edge kernels with learning-based rigid and non-rigid registration techniques. Unlike conventional layers that learn all features without specific bias, our approach begins with a predefined edge detection kernel, which is then perturbed with random noise. These kernels are learned during training to extract optimal edge features tailored to the task. This adaptive edge detection enhances the registration process by capturing diverse structural features critical in medical imaging. To provide clearer insight into the contribution of each component in our design, we introduce four variant models for rigid registration and four variant models for non-rigid registration. We evaluated our approach using a dataset provided by the Medical University across three setups: rigid registration without skull removal, with skull removal, and non-rigid registration. Additionally, we assessed performance on two publicly available datasets. Across all experiments, our method consistently outperformed state-of-the-art techniques, demonstrating its potential to improve multi-modal image alignment and anatomical structure analysis.