MULTISCALE IMAGE ENHANCEMENT WITH RUSCHEWEYH COEFFICIENT BASED MASKS
16TH INTERNATIONAL ARTEMIS SCIENTIFIC RESEARCH CONGRESS, Bucuresti, Romanya, 28 - 30 Ağustos 2026, ss.1007-1020, (Tam Metin Bildiri)
- Yayın Türü: Bildiri / Tam Metin Bildiri
- Basıldığı Şehir: Bucuresti
- Basıldığı Ülke: Romanya
- Sayfa Sayıları: ss.1007-1020
- İstanbul Gelişim Üniversitesi Adresli: Evet
Özet
The coefficients of convolution masks used in image enhancement are often selected empirically. This reduces mathematical interpretability. It also makes scale selection difficult. Geometric function theory provides a systematic design basis through the coefficients of normalized analytic functions. This study investigates how the size of a Ruscheweyh coefficient-based mask affects image quality and processing time. The main aim is to determine whether a larger mask size provides a consistent advantage under different blur levels. The Koebe function f1(z)=z/(1−z)2 , the convex extremal function f2(z)=z/(1−z), and the bounded turning extremal function f3(z)=−z−2log(1−z) were used. For f(z) = z + ∑ an ∞ n=2 zn, the transformed coefficients were defined by cn(δ)=[(δ+1)n−1/(n−1)!]an. Symmetric 3×3, 5×5, and 7×7 masks were then constructed. The k-th ring was assigned the value −ck+1(δ). The center coefficient was selected as CR(δ) = 1 + ∑ 8k · ck+1(δ) R k=1 , where R is the number of rings. The sum of every mask was therefore equal to one. This condition ensures that regions of constant gray level are preserved. The camera, coins, and moon images were used in the experiments. Gaussian blur levels of σ=1.0, 1.5, and 2.0 were applied. Six Ruscheweyh parameter values between δ=−0.9 and δ=0.0 were tested for each function and mask size. A total of 486 enhancement experiments were performed. The enhanced images were compared with the reference images by the structural similarity index measure (SSIM) and the peak signal-to-noise ratio (PSNR). Convolution time was also recorded. The 3×3 masks ranked first at all blur levels. Their mean best SSIM and PSNR values were 0.9071 and 33.46 dB. The corresponding values were 0.8967 and 32.56 dB for the 5×5 masks, and 0.8870 and 32.06 dB for the 7×7 masks. The best fixed configuration over all images and blur levels was the 3×3 Koebe mask at δ=−0.7. It achieved a mean SSIM of 0.8948 and a mean PSNR of 32.49 dB. These correspond to gains of 0.0557 in SSIM and 1.73 dB in PSNR over the blurred inputs. The best blur-specific configurations were the 3×3 convex mask at δ=−0.7 for σ=1.0, the 3×3 convex mask at δ=−0.1 for σ=1.5, and the 3×3 Koebe mask at δ=−0.3 for σ=2.0. Mean convolution times were 4.72, 9.18, and 16.74 ms for the 3×3, 5×5, and 7×7 masks. The results show that a larger mask does not always improve image quality: although higher-order rings increase sharpening strength, they also raise both the sensitivity to δ and the computational cost. The study establishes an interpretable multiscale framework that links Ruscheweyh coefficients, blur level, mask size, and image enhancement performance.
Keywords: Geometric function theory (GFT), image enhancement, Ruscheweyh operator, multiscale convolution mask, univalent functions.