Image segmentation based on discontinuities in intensity focuses on detecting points, lines, and edges in an image.
These features are characterized by abrupt changes in pixel values and are detected using derivatives.
1. Definitions:
- Edge Pixel: A pixel where image intensity changes sharply.
- Edge Segment: A group of connected edge pixels.
- Line: A thin set of pixels with intensity much higher or lower than its background (gives rise to “roof edges”).
- Isolated Point: A single pixel different in intensity from its neighbors.
2. Role of Derivatives in Detection:
Derivatives help detect intensity changes:
- First-order derivative: Detects changes in intensity (produces thick edges).
- Second-order derivative: Detects rate of change of intensity (produces thin edges and reacts more strongly to fine details).
3. Derivative Conditions:
First-order derivatives:
- Zero in flat regions.
- Non-zero at the start and along a ramp.
Second-order derivatives:
- Zero in flat regions and along a ramp.
- Non-zero only at the start and end of a ramp.
4. Approximating Derivatives in Digital Images
First-Order Derivatives (using finite differences):
5. Example: Edge Profile Analysis (Ref: Fig. 10.2)
- Ramp Edge: Gradual intensity change →
- First derivative: constant non-zero.
- Second derivative: spike at start & end.
- Step Edge: Sudden jump in intensity →
- First derivative: single peak.
- Second derivative: double peak (positive and negative).
- Isolated Point:
- Strong second derivative response.
- Line (thin object):
- Detected more by second-order derivative (fine detail).
