IMAGE ENHANCEMENT WITH RUSCHEWEYH COEFFICIENT BASED 5×5 MASKS
16TH INTERNATIONAL ARTEMIS SCIENTIFIC RESEARCH CONGRESS, Bucuresti, Romanya, 28 - 30 Ağustos 2026, ss.995-1006, (Tam Metin Bildiri)
- Yayın Türü: Bildiri / Tam Metin Bildiri
- Basıldığı Şehir: Bucuresti
- Basıldığı Ülke: Romanya
- Sayfa Sayıları: ss.995-1006
- İstanbul Gelişim Üniversitesi Adresli: Evet
Özet
The coefficients of convolution masks used in image enhancement are often selected empirically. This limits the mathematical interpretability of the resulting filters. Geometric function theory provides a systematic design basis through the coefficients of normalized analytic functions. In this study, threea 5×5 image enhancement masks were constructed with the Ruscheweyh operator. 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 selected as extremal functions. The coefficients obtained from their Taylor series expansions are an=n, an=1 and an=2/n for n≥2, respectively. The Ruscheweyh derivative operator is a Hadamard convolution operator. The operator is defined as the Hadamard product of a function f ∈ A with the kernel function z/(1−z)(δ+1). Here the condition δ>−1 holds. The second and third Taylor coefficients of the Ruscheweyh derivatives of f1, f2 and f3 are therefore c2(δ)=(δ+1)a2 and c3(δ)=[(δ+1)(δ+2)/2]a3. These coefficients were assigned with negative signs to the inner ring of eight cells and to the outer ring of sixteen cells, respectively. The center coefficient was taken as C(δ)=1+8c2(δ)+16c3(δ). The mask sum was therefore equal to one. This condition preserved the constant gray level. Three grayscale images from scikit-image camera, coins and moon were blurred with a Gaussian kernel of σ=1.5, filtered with each mask, and compared against the references using SSIM and PSNR. Nine δ values in [−0.9, 1] were tested for each of the three functions. The mean SSIM of the blurred images was 0.834. The highest mean SSIM was 0.8922 for f3 at δ=−0.7. The highest mean PSNR was 32.50 dB for f2 at δ=−0.9. The results show that the function class determines the coefficient profile of the mask. The parameter δ determines the strength of this profile. The findings are limited to three images and a single degradation level. They are therefore exploratory. The proposed approach establishes a reproducible and interpretable link between geometric function theory and convolution mask design.
Keywords: Geometric function theory (GFT), image enhancement, Ruscheweyh operator, convolution mask, univalent functions.