Q12Digital Image Processing

Point processing (intensity transformation) techniques are zero-memory operations where the new value $s$ of a pixel depends solely on its original intensity $r$, expressed as $s=T(r)$, independent of pixel location or neighboring pixels.

• Image Negative: Computed as $s=(L-1)-r$ for an image with $L$ gray levels; useful for enhancing white or gray detail embedded in dark regions, such as in medical imaging.
• Log Transformation: Given by $s=c\log (1+r)$; it compresses the dynamic range by expanding dark pixel values while compressing bright ones, useful for displaying Fourier spectra with large dynamic range.
• Power-Law (Gamma) Transformation: Given by $s=c{r}^{\gamma }$; when $\gamma <1$ it expands dark regions (used for display gamma correction of CRT monitors, which have $\gamma \approx 2.5$), and when $\gamma >1$ it expands bright regions.
• Contrast Stretching: A piecewise-linear function that expands the range of intensity levels so that low-contrast images (from poor illumination or sensor limitations) span the full dynamic range, sharply increasing visual contrast.
• Gray-Level (Intensity) Slicing: Highlights a specific range of gray levels, either setting them to a high value while leaving others unchanged, or setting them to high value while suppressing all others to black; used to highlight features like flaws in an X-ray.

These transformations are commonly visualized and implemented using lookup tables (LUTs), making them computationally very fast to apply across an entire image, since the mapping $T(r)$ for each of the 256 possible gray levels is precomputed once and then applied to every pixel with a single table lookup rather than a repeated arithmetic operation.

A practical example clarifies the effect of gamma correction: for an 8-bit image with $r$ normalized to $[0,1]$, applying $\gamma =0.4$ to a mid-gray pixel $r=0.5$ gives $s=0.5^{0.4}\approx 0.76$, brightening it substantially, whereas $\gamma =2.5$ gives $s=0.5^{2.5}\approx 0.177$, darkening it. This is precisely why display devices apply an inverse gamma correction before rendering, so that the perceived brightness matches the linear intensity captured by the sensor.