1. Zoomed clip of the TRANSPARENT layer created in Photoshop and Gaussian Blur with 0.6 radius applied.
White background is just another layer rendered with white.

2. Zoomed clip of the image generated with GDI+ on a WHITE bitmap with Gaussian Blur filter - 3x3
convolution matrix. PERFECT!

3. Zoomed clip of the image generated with GDI+ on a TRANSPARENT bitmap with Gaussian Blur filter - 3x3
convolution matrix. White background was added for the contrast later on. Transparent pixels are somewhat grayish