Non-local means (NL-means) is a state-of-the-art image denoising algorithm that leverages self-similarity by averaging similar patches weighted by the classic $L_2$-norm distance. In this work, we extend the similarity measure to arbitrary $L_p$-norms ($1 \le p \le \infty$) and investigate their impact on denoising performance. We implement and evaluate NL-means with $p = 1, 2, 3, 4, \infty$ and compare via quantitative metrics (MSE, MAE, PSNR, SSIM), residual analysis, and visual inspection. Experiments on the \emph{Lena} image corrupted with AWGN ($\sigma = 20$), a widely used benchmark setting in the denoising literature, show that while $L_2$-norm remains optimal overall, other norms off... More >