CS654: Digital Image Analysis Lecture 40: Miscellaneous topics

Geometric transformations About origin About an arbitrary point About a line

Pixel arrangement

Invariance

Scaling and interpolation

Scaling and interpolation

Sampling

New image

6-Connectivity

Color Model

Mask based edge detection Smooth the input image 𝑓 𝑥,𝑦 =𝑓 𝑥,𝑦 ∗𝐺 𝑥,𝑦 𝑓 𝑥 𝑥,𝑦 = 𝑓 𝑥,𝑦 ∗ 𝑀 𝑥 𝑥,𝑦 𝑓 𝑦 𝑥,𝑦 = 𝑓 𝑥,𝑦 ∗ 𝑀 𝑦 𝑥,𝑦 |𝛻𝑓|= 𝑓 𝑥 𝑥,𝑦 +| 𝑓 𝑦 𝑥,𝑦 | 𝜃= tan −1 𝑓 𝑥 𝑥,𝑦 𝑓 𝑦 𝑥,𝑦 𝐼𝑓 𝑚𝑎𝑔𝑛(𝑥, 𝑦)>𝑇,𝑡ℎ𝑒𝑛 𝑝𝑜𝑠𝑠𝑖𝑏𝑙𝑒 𝑒𝑑𝑔𝑒 𝑝𝑜𝑖𝑛𝑡 𝒇 𝒚 𝜵𝒇 𝜽 𝒚+𝟏 38 66 65 14 35 64 12 15 42 𝒚 𝒇 𝒙 𝒚−𝟏 𝒙−𝟏 𝒙 𝒙+𝟏

Numerical Example

Numerical Example: Separable?

Segmentation The grey level values of the object and the background pixels are distributed according to the probability density function: 𝒑 𝒙 = 𝟑 𝟒 𝒂 𝟑 𝒂 𝟐 − 𝒙−𝒃 𝟐 𝒇𝒐𝒓 𝒃−𝒂≤𝒙≤𝒃+𝒂 𝟎, 𝒐𝒕𝒉𝒆𝒓𝒘𝒊𝒔𝒆 with a = 1, b = 5 for the background and a = 2, b = 7 for the object. Sketch the two distributions and determine the range of possible thresholds.

Segmentation

Weight of a 3×3 matrix for edge detection

Mask design Line detection kernels which respond maximally to horizontal, vertical and oblique single pixel wide lines -1 2 -1 2 -1 2 2 -1 Horizontal Vertical +45o -45o

Mask processing -1 2 -1 2 -1 2 ⊗