Nonlinear Stretching

• Nonlinear functions with a fixed form
• Fewer parameters to adjust
• Satisfying $0=f_{\min} \leq g \leq f_{\max} =L-1$
• Examples
  • Logarithmic transformation: $g=b \log(af +1)$
    • Stretch dark region, suppress bright region
  • Exponential transformation: $g=b(e^{af}-1)$
    • Expand bright region
  • Power Law: $g=af^k$
    • $K=2$: square law, similar to exponential
    • $K=1/3$: cubic root, similar to logarithmic

See: Point-Wise Transformation