Fuzzy Techniques for Image Segmentation Outline ... - SSIP-2013

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Fuzzy Techniques for Image Segmentation László G. Nyúl FC with threshold CT and MRA Fuzzy Techniques for Image Segmentation László G. Nyúl Fuzzy connectedness variants Outline Outline Fuzzy systems Fuzzy sets Fuzzy systems Fuzzy sets • Multiple seeds per object Fuzzy image processing Fuzzy connectedness Theory Algorithm Variants Applications Fuzzy image processing Fuzzy connectedness Theory Algorithm Variants Applications • Scale-based fuzzy affinity • Vectorial fuzzy affinity • Absolute fuzzy connectedness • Relative fuzzy connectedness • Iterative relative fuzzy connectedness Fuzzy Techniques for Image Segmentation Scale-based affinity Fuzzy Techniques for Image Segmentation Scale-based affinity László G. Nyúl László G. Nyúl Outline Outline Fuzzy systems Fuzzy systems Fuzzy sets Fuzzy image processing Fuzzy connectedness Theory Algorithm Variants Applications Considers the following aspects • spatial adjacency • homogeneity (local and global) • object feature (expected intensity properties) • object scale Fuzzy sets Fuzzy image processing Fuzzy connectedness Theory Algorithm Variants Applications Considers the following aspects • spatial adjacency • homogeneity (local and global) • object feature (expected intensity properties) • object scale
Fuzzy Techniques for Image Segmentation Object scale Fuzzy Techniques for Image Segmentation Computing object scale László G. Nyúl Outline Fuzzy systems Fuzzy sets Fuzzy image processing Fuzzy connectedness Theory Algorithm Variants Applications Object scale in C at any spel c ∈ C is the radius r(c) of the largest hyperball centered at c which lies entirely within the same object region László G. Nyúl Outline Fuzzy systems Fuzzy sets Fuzzy image processing Fuzzy connectedness Theory Algorithm Variants Applications Algorithm Input: C, c ∈ C, W ψ , τ ∈ [0, 1] Output: r(c) begin k ← 1 while FO k (c) ≥ τ do k ← k + 1 endwhile r(c) ← k end The scale value can be simply and effectively estimated without explicit object segmentation Fraction of the ball boundary homogeneous with the center spel ∑ W ψs (|f (c) − f (d)|) FO k (c) = d∈B k (c) |B k (c) − B k−1 (c)| Fuzzy Techniques for Image Segmentation László G. Nyúl Relative fuzzy connectedness Fuzzy Techniques for Image Segmentation László G. Nyúl Relative fuzzy connectedness Algorithm Outline Fuzzy systems Fuzzy sets Fuzzy image processing Fuzzy connectedness Theory Algorithm Variants Applications • always at least two objects • automatic/adaptive thresholds on the object boundaries • objects (object seeds) “compete” for spels and the one with stronger connectedness wins Outline Fuzzy systems Fuzzy sets Fuzzy image processing Fuzzy connectedness Theory Algorithm Variants Applications Let O 1 ,O 2 ,...,O m , a given set of objects (m ≥ 2), S = {o 1 ,o 2 ...,o m } a set of corresponding seeds, and let b(o j ) = S \ {o j } denote the ‘background’ seeds w.r.t. seed o j . 1 define affinity for each object ⇒ κ 1 ,κ 2 ,...,κ m 2 combine them into a single affinity ⇒ κ = ⋃ j κ j 3 compute fuzzy connectedness using κ ⇒ K 4 determine the fuzzy connected objects ⇒ O ob (o) = {c ∈ C | ∀o ′ ∈ b(o) µ K (o,c) > µ K (o ′ ,c)} { η(c) if c ∈ O ob (o) µ Oob (c) = 0 otherwise
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Fuzzy Techniques for Image Segmentation Outline ... - SSIP-2013

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