1. Secrets of GrabCut and Kernel K-means
Meng Tang1 Ismail Ben Ayed2 Dmitrii Marin1 Yuri Boykov1
1University of Western Ontario, Canada University of Quebec, Canada
GrabCut as Color Clustering
Probabilistic K-means vs Kernel K-means
Our Energy Formulation & Optimization
Initialization
Basic K-means (e.g. Chan-Vese)
Variance Criterion
Kernel K-means plus smoothness regularization:
Pairwise clustering term
MRF regular.
GMMs fitting
more complex
data representation
probability models
solution space S St
St+1
At(S)
E(S)
E(St)
E(St+1)
bound optimization for E(S)
unary bound for kernel k-means[4]
minimize bound with graph cuts
Probabilistic K-means (e.g. Zhu&Yuille, GrabCut[1])
kernel K-means[4] (ours)
3D color space
descriptive GMMs over-fit the data
sensitive to local minima
log-likelihoods with parametric probability
Model parameters θ often jointly optimized
Experiments of GrabCut and our KKM
Kernel give implicit feature
Model-fitting & Kernel K-means
Low dimension: RGB only
GrabCut
KKM
aKKM
Box and GT
example θ : descriptive models (histogram or GMM)
example k : normalized Gaussian (fixed small width)
GrabCut
KKM A B C
Smoothness map
Entropy Criterion
Gini Criterion
H(S) - entropy for intensities in S
G(S) – Gini impurity for intensities in S
(a) initialization
(b) K-means
(c) Elliptic K-means
intensity histogram
Solution A
Solution B
Secrets of Kernel K-means:
the bias of optimal
Gini clustering
(see Breiman [3], for histograms)
Figure 1: Robustness to regularization weight
Figure 2: sample results on GrabCut dataset
(d) Histogram fitting
(e) GMM: local mini.
(f) GMM: from G.T.
bias to small & dense cluster
observed for average association
in [2]. We extend Breiman’s
analysis [3] to continuous case
common adaptive kernels (e.g. KNN)
eliminate such bias (see paper)
High dimension: RGBD (depth)
depth map
GrabCut
Our aKKM
solution A and B are equally
good when using histograms
local minima issue using GMMs
(g) K-mode (mean-shift)
(h) Our Kernel K-means
model-fitting: local min., binning
kernel K-means: non-linear separa.
Figure 4: Scalability to higher
dimension on RGB+wD
Figure 3: Average error on
GrabCut dataset
High dimension feature : RGBXYM (location XY, motion M)
Proposed Kernel K-means
“World Map” of Segmentation
Fixed Gaussian Kernel
pKM
Probabilistic K-means
(ML model fitting)
kKM
kernel K-means
(average distortion AD or association AA)
basic K-means
p.s.d. kernel
weak
kernel clustering
(unary) Hilbertian distortion
Normalized Cuts
K-modes
(mean-shift)
GMM fitting
histogram fitting
geometric fitting
gamma fitting
Gaussian kernel
K-means
Spectral clustering
distortion
Gibbs fitting
Average Cut
Gini Bias
Adaptive Kernel
good clustering
(a)Video frames
(b)Optical flow
(c)Our aKKM(RGBXY)
(d)Our aKKM(RGBXYM)
[1] C. Rother, V. Kolmogorov and A. Blake, GrabCut: Interactive Foreground
Extraction using Iterated Graph Cuts, in SIGGRAPH 2004.
[2] J. Shi, and J. Malik. Normalized cuts and image segmentation. IEEE Transactions
on Pattern Analysis and Machine Intelligence (PAMI), 22: , 2000.
[3] L. Breiman. Technical note: Some properties of splitting
criteria. Machine Learning, 24(1):41-47, 1996.
[4] I. Dhillon, Y. Guan, and B. Kulis. Kernel K-means, spectral
clustering and normalized cuts. In KDD, 2004.