vc2_bit_widths

The vc2_bit_widths Python package provides routines for computing how many bits of numerical precision are required for implementations of the SMPTE ST 2042-1:2017 VC-2 professional video codec. In addition it also provides routines for producing test pictures which produce large signal values in actual video codecs.

This manual is split into three parts. In User’s Manual a general introduction to the purpose, terminology and usage of this module is given. In Theory and Design, the underlying theory and mathematical approach are described and evaluated. Finally, Internals and Low-Level API gives a more detailed overview of the implementation and lower-level features of this software.

Finally, you can find the source code for vc2_bit_widths on GitHub.

Note

This documentation is also available in PDF format.

User’s Manual

• Introduction
  • Caveats
  • Terminology
• Tutorial
  • Static filter analysis
  • Calculating bit-width requirements
  • Bounding quantisation indices
  • Optimising synthesis test patterns
  • Generating test pictures
  • Bundling analyses and test pattern data files
• Command-line utilities reference
  • vc2-static-filter-analysis
  • vc2-static-filter-analysis-combine
  • vc2-bit-widths-table
  • vc2-bit-width-test-pictures
  • vc2-maximum-quantisation-index
  • vc2-optimise-synthesis-test-patterns
  • vc2-bundle
• High-level Python API Reference
  • vc2_bit_widths.helpers: Helper Functions
  • vc2_bit_widths.patterns: Containers for test pattern data
  • vc2_bit_widths.json_serialisations: JSON Data File Serialisation/Deserialisation
  • vc2_bit_widths.bundle: Analysis file bundling

Theory and Design

• Theory overview
• Related work
• Computing signal bounds with Affine Arithmetic
  • Analysing linear filters
  • Affine arithmetic
  • Worked example
  • Quantisation and affine arithmetic
  • Refining worst-case quantisation error bounds
• Test pattern generation
  • Analysis filter test patterns
  • Synthesis filter test patterns
• Experimental results
  • Heuristic vs naive synthesis test patterns
  • Comparison with natural images and noise

Internals and Low-Level API

• Low-level API Overview
  • Evaluation and deployment of test patterns
  • Calculating signal bounds and test patterns
  • Specialised partial evaluation functions for VC-2 filters
  • Implementations of VC-2’s quantiser and wavelet filters
  • Utilities for representing and implementing filter behaviour
• vc2_bit_widths.pattern_evaluation: Measure the outputs achieved by test patterns
  • Evaluation functions
  • Utility functions
• vc2_bit_widths.picture_packing: Pack test patterns into pictures
  • API
  • Example output
• vc2_bit_widths.signal_bounds: Finding bounds for filter output values
  • Finding signal bounds
  • Integer representation utilities
• vc2_bit_widths.pattern_generation: Heuristic test pattern generation
  • Test pattern generators
• vc2_bit_widths.pattern_optimisation: (Synthesis) Test Pattern Optimisation
  • Search algorithm & parameters
  • API
• vc2_bit_widths.fast_partial_analysis_transform: Wavelet analysis transform
  • Example usage
  • API
• vc2_bit_widths.fast_partial_analyse_quantise_synthesise: Fast single value encode, quantise and decode
  • Example usage
  • API
• vc2_bit_widths.quantisation: VC-2 Quantisation
  • Quantisation & dequantisation
  • Analysis
• vc2_bit_widths.vc2_filters: VC-2 Filters Implemented as InfiniteArrays
  • Usage
  • Omitting arrays
  • API
• vc2_bit_widths.linexp: A simple Computer Algebra System with affine arithmetic
  • Linear expressions
  • Usage
  • Affine Arithmetic
  • API
• vc2_bit_widths.pyexp: Construct Python programs implementing arithmetic expressions
  • Motivation
  • Getting started
  • Carving functions out of existing code
  • Manipulating expressions
  • API
• vc2_bit_widths.infinite_arrays: Infinite arrays
  • Tutorial
  • API