Circular separable convolution depth of field

Abstract

Circular Separable Convolution Depth of Field (CSC DoF) is a mathematical adaptation and implementation of a separable circular filter, which utilizes complex plane phasors to create very accurate and fast bokeh. At its core, this technique convolves a circular pattern blur in the frequency domain using a horizontal and a vertical pass, representing the frame buffer using complex numbers. This technique renders at magnitudes faster than brute-force and sprite-based approaches, since it is a separable convolution. Important properties of this technique include convolution separability, low memory bandwidth and large radii circles. The technique has been shipped on Madden NFL 15, Madden NFL 16, Madden NFL 17, Fifa 17 and PGA Tour Rory McIlroy. The implementation includes an offline shader code generation step containing pre-computed frequency domain filters, multiple weighted passes for imaginary and real number processing. We will present the mathematical derivation and some caveats to achieve the required precision for intermediate frequency domain frame buffers.