superpixels and polygons using simple non-iterative ... · simple non-iterative clustering (snic)...

SNIC makes two important modiﬁcations to SLIC : 1. Centroids are evolved using online averaging. 2. Label assignment is achieved using a priority queue, which returns the element with the shortest distance D to a centroid. Polygon Partitioning Algorithm 1. Segment image. Trace superpixel boundaries using a standard algorithm. 2. Assign initial vertices to be pixels that touch at least three different segments, at least two segments and the image borders, or are image corners. 3. New vertices are added using the Douglas-Peucker curve simpliﬁcation algorithm. 4. Merge vertices that are too close and join remaining vertices to obtain polygons. 1. Pick seeds on a regular square grid. 2. Initialize priority queue Q with immediate neighbors of seeds. While Q is not empty: 3. Pop Q, and label the pixel P. 4. Update corresponding centroid. 5. For all unlabeled neighbors of P, compute D and push on Q. |Q| = 16 +16 2. For each seed compute distance D to unlabeled neighbors and push on Q. -1 |Q| = 15 3. Pop the top-most element on the queue and label the corresponding pixel. 4. Compute distance D to the nearest neighbors of this newly labeled pixel and push on Q. Continue until Q is empty. |Q| = 18 +3 1. Initial seeds with a unique label. Q is empty at this time. |Q| =0 Unlabeled pixel Labeled pixel Simple Non-Iterative Clustering (SNIC) is an improved version of the Simple Linear Iterative Clustering* (SLIC) algorithm. SNIC is non- iterative, enforces connectivity from the start, requires less memory, is faster, and yet is a simpler algorithm. On segmentation benchmarks SNIC performs better than the state-of-the-art, including SLIC. s ⇥ s s ⇥ s 2s ⇥ 2s Local k-means (SLIC) Shortcomings of SLIC: 1. Several iterations 2. Repeat computations in overlapping local regions 3. Pixel connectivity enforced as a post-processing step SLIC review D = kx j - x j k 2 2 s + kc j - c k k 2 2 m c =[l, a, b] T x =[x, y ] T s = r N K m = 10 SLIC performs k-means clustering on the image plane with centroids chosen on a square grid in the image plane and distance D to be a weighted sum of the normalized spatial and color distances. Superpixels and Polygons using Simple Non-Iterative Clustering RADHAKRISHNA ACHANTA & SABINE SÜSSTRUNK Simple Non-Iterative Clustering (SNIC) Algorithm SNIC superpixels SNIC polygons IVRL (IC), EPFL Global k-means * SLIC Superpixels Compared to the State-of-the-art Superpixel Methods. R. Achanta, S. Shaji, K. Smith, A. Lucchi, P. Fua. S. Süsstrunk (TPAMI 2012). 200 400 600 800 1000 1200 1400 1600 1800 2000 Number of superpixels 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.12 Segmentation error (CUSE) NCUTS MST TURBO SLIC SEEDS ERS LSC SNIC CONPOLY SNICPOLY 200 400 600 800 1000 1200 1400 1600 1800 2000 Number of superpixels 0.28 0.29 0.3 0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 F-measure NCUTS MST TURBO SLIC SEEDS ERS LSC SNIC CONPOLY SNICPOLY 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 Boundary recall 0.6 0.65 0.7 0.75 0.8 0.85 0.9 Boundary precision NCUTS MST TURBO SLIC SEEDS ERS LSC SNIC CONPOLY SNICPOLY

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Page 1: Superpixels and Polygons using Simple Non-Iterative ... · Simple Non-Iterative Clustering (SNIC) is an improved version of the ... SLIC performs k-means clustering on the image plane

SNIC makes two important modifications to SLIC : 1. Centroids are evolved using online averaging. 2. Label assignment is achieved using a priority queue, which returns the element with the shortest distance D to a centroid.

Polygon Partitioning Algorithm

1. Segment image. Trace superpixel boundaries using a standard algorithm.

2. Assign initial vertices to be pixels that touch at least three different segments, at least two segments and the image borders, or are image corners.

3. New vertices are added using the Douglas-Peucker curve simplification algorithm.

4. Merge vertices that are too close and join remaining vertices to obtain polygons.

1.  Pick seeds on a regular square grid. 2.  Initialize priority queue Q with immediate neighbors of seeds.

While Q is not empty: 3. Pop Q, and label the pixel P. 4. Update corresponding centroid. 5. For all unlabeled neighbors of P, compute D and push on Q.

|Q| = 16

+16

2. For each seed compute distance D to unlabeled neighbors and push on Q.

�1

|Q| = 15

3. Pop the top-most element on the queue and label the corresponding pixel.

4. Compute distance D to the nearest neighbors of this newly labeled pixel and push on Q. Continue until Q is empty.

|Q| = 18

1. Initial seeds with a unique label. Q is empty at this time.

|Q| = 0

Unlabeled pixel Labeled pixel

Simple Non-Iterative Clustering (SNIC) is an improved version of the Simple Linear Iterative Clustering* (SLIC) algorithm. SNIC is non-iterative, enforces connectivity from the start, requires less memory, is faster, and yet is a simpler algorithm. On segmentation benchmarks SNIC performs better than the state-of-the-art, including SLIC.

s⇥ s s⇥ s

2s⇥ 2s

Local k-means (SLIC)

Shortcomings of SLIC: 1.  Several iterations 2.  Repeat computations in overlapping local regions 3.  Pixel connectivity enforced as a post-processing step

SLIC review

D =kxj � xjk22

kcj � ckk22m

c = [l, a, b]Tx = [x, y]T s =

Km = 10

SLIC performs k-means clustering on the image plane with centroids chosen on a square grid in the image plane and distance D to be a weighted sum of the normalized spatial and color distances.

Superpixels and Polygons using Simple Non-Iterative Clustering RADHAKRISHNA ACHANTA & SABINE SÜSSTRUNK

Simple Non-Iterative Clustering (SNIC) Algorithm

SNIC superpixels SNIC polygons

IVRL (IC), EPFL

Global k-means

* SLIC Superpixels Compared to the State-of-the-art Superpixel Methods. R. Achanta, S. Shaji, K. Smith, A. Lucchi, P. Fua. S. Süsstrunk (TPAMI 2012).

200 400 600 800 1000 1200 1400 1600 1800 2000

Number of superpixels0.02

0.03

0.04

0.05

0.06