bc7f: Prediction, Not Search

The bc7f encoder relies on an analytical, statistics-driven error model rather than iterative search. This O(1) real-time encoder exploits simple closed-form expressions to predict which BC7 mode family (4/5, 0/2, 1/3/7, or 6) is worth considering. It then estimates the block’s SSE/MSE for each candidate using lightweight block statistics derived from covariance analysis together with the mode’s weight and endpoint quantization characteristics. All of this is performed prior to encoding any BC7 modes. In purely analytical mode, bc7f predicts, encodes a single BC7 block, and returns.

BC7 block decoding is an affine interpolation between quantized endpoints using quantized weights, which allows first-order error propagation to be modeled directly. For a given block, the encoder computes basic statistics such as the mean and covariance of the input texels; the principal axis derived from the covariance is used both for endpoint fitting and to estimate the orthogonal least-squares (“line fit”) residual error as trace(covariance) − λ₁. Quantization noise from endpoints and weights is modeled independently using uniform quantization assumptions, with endpoint error contributing an additive term and weight/index error contributing a span-dependent term proportional to the squared endpoint distance. These closed-form estimates are sufficient to predict relative SSE across BC7 mode families, partitions, and dual-plane configurations without trial encodes. As a result, bc7f can select parameters and emit a single BC7 block in strictly bounded time, producing deterministic, high-quality results without brute-force search or refinement.

bc7f is significantly faster than bc7e.ispc Level 1, but because it exploits the entire BC7 format, it isn’t as brittle. The follow-up, “bc7g” is in the works.

Binomial first developed these techniques for our ASTC encoders, and later used them to implement bc7f. We expect these predictive, analytical encoding techniques to be rapidly adopted.