Systems, Man & Cybernetics - April 2017 - 20

Training Set

FLAIR

T2 T1c
T1

Kernel Sparse Representation

...
Slice 1

Kernel
Dictionary
Learning

Slice N

Preprocessing
Test Set

FLAIR

T2 T1c
T1

Training Phase
Multichannel Superpixel-Level
Features Exaction and Fusion

Slice M

Ground Truth

Class-Specific
Dictionaries
Kernel
Sparse
Coding

T1c

...
Slice 1

T1c

Test Phase
Result

Segmentation
Postprocessing

Graph-Cuts
Test Phase

Figure 1. an overview of the proposed automated framework for multilabel brain tumor segmentation.
the dashed and solid arrows indicate the pipelines in the training phase and the test phase, respectively.

where X denotes the sparse code
extraction of superpixel-level features, including multichannel hismatrix;
D, the dictionary; <$< F the
Magnetic resonance
tograms and spatial location. The
Frobenius norm; <$< 0 the , 0 norm,
imaging is the most
extracted superpixel-level features
and T0, the sparsity level [9]. The
are mapped to the feature space
sparsity level indicates the maxicommon technology
F with a nonlinear transformamum number of nonzero entries in
in brain imaging due
tion U ($), where the non linear
a sparse code x i . The optimization
to its advantages in
of this objective function gives a
similarity between two samples
learned dictionary for the training
are more discriminative than their
terms of safety, tissue
samples in F space and optimal
linear similarity in the original
contrast, and fewer
sparse codes for samples with
space, and hence more discriminarespect to the dictionary.
tive sparse represen tations can
artifacts compared
In the training phase, kernelbe expected. As mentioned, the
to other modalities,
dictionary learning leads to classnonlinear similarity, which is
such as computed
specific dictionar ies that are
computed by the inner product
T
l
optimized for each task-relevant
U (x) U (x ) in F , given two samtomography.
class, i.e., nontumor, necrotic core,
ples x and xl , can be easily calcuedema, nonenhancing core, and
lated with a predefined kernel
enhancing core (labels 1 to 5,
function K. The kernel trick also
respectively) in our application. These dictionaries
facilitates the fusion of multifeatures in such a way that it
should be able to model their own classes well, even
can be fulfilled by a simple entry-wise product. The fusion
though they fail to well approximate the rest of the classenables the dictionary-learning process to capture several
es. In the test phase, these learned dictionaries are used
features at the same time.
in the generation of kernel sparse representations for
To adapt sparse coding and dictionary learning in featest samples. If a test sample belongs to a specific class,
ture space, their kernel extensions are used. Given a data
the smallest approximation error can be achieved when
matrix Y, the objective function is expressed as:
the dictionary learned for this class is used in kernel
t,D
t ) = arg min 



Table of Contents for the Digital Edition of Systems, Man & Cybernetics - April 2017

Systems, Man & Cybernetics - April 2017 - Cover1

Systems, Man & Cybernetics - April 2017 - Cover2

Systems, Man & Cybernetics - April 2017 - 1

Systems, Man & Cybernetics - April 2017 - 2

Systems, Man & Cybernetics - April 2017 - 3

Systems, Man & Cybernetics - April 2017 - 4

Systems, Man & Cybernetics - April 2017 - 5

Systems, Man & Cybernetics - April 2017 - 6

Systems, Man & Cybernetics - April 2017 - 7

Systems, Man & Cybernetics - April 2017 - 8

Systems, Man & Cybernetics - April 2017 - 9

Systems, Man & Cybernetics - April 2017 - 10

Systems, Man & Cybernetics - April 2017 - 11

Systems, Man & Cybernetics - April 2017 - 12

Systems, Man & Cybernetics - April 2017 - 13

Systems, Man & Cybernetics - April 2017 - 14

Systems, Man & Cybernetics - April 2017 - 15

Systems, Man & Cybernetics - April 2017 - 16

Systems, Man & Cybernetics - April 2017 - 17

Systems, Man & Cybernetics - April 2017 - 18

Systems, Man & Cybernetics - April 2017 - 19

Systems, Man & Cybernetics - April 2017 - 20

Systems, Man & Cybernetics - April 2017 - 21

Systems, Man & Cybernetics - April 2017 - 22

Systems, Man & Cybernetics - April 2017 - 23

Systems, Man & Cybernetics - April 2017 - 24

Systems, Man & Cybernetics - April 2017 - 25

Systems, Man & Cybernetics - April 2017 - 26

Systems, Man & Cybernetics - April 2017 - 27

Systems, Man & Cybernetics - April 2017 - 28

Systems, Man & Cybernetics - April 2017 - 29

Systems, Man & Cybernetics - April 2017 - 30

Systems, Man & Cybernetics - April 2017 - 31

Systems, Man & Cybernetics - April 2017 - 32

Systems, Man & Cybernetics - April 2017 - 33

Systems, Man & Cybernetics - April 2017 - 34

Systems, Man & Cybernetics - April 2017 - 35

Systems, Man & Cybernetics - April 2017 - 36

Systems, Man & Cybernetics - April 2017 - 37

Systems, Man & Cybernetics - April 2017 - 38

Systems, Man & Cybernetics - April 2017 - 39

Systems, Man & Cybernetics - April 2017 - 40

Systems, Man & Cybernetics - April 2017 - 41

Systems, Man & Cybernetics - April 2017 - 42

Systems, Man & Cybernetics - April 2017 - 43

Systems, Man & Cybernetics - April 2017 - 44

Systems, Man & Cybernetics - April 2017 - 45

Systems, Man & Cybernetics - April 2017 - 46

Systems, Man & Cybernetics - April 2017 - 47

Systems, Man & Cybernetics - April 2017 - 48

Systems, Man & Cybernetics - April 2017 - 49

Systems, Man & Cybernetics - April 2017 - 50

Systems, Man & Cybernetics - April 2017 - 51

Systems, Man & Cybernetics - April 2017 - 52

Systems, Man & Cybernetics - April 2017 - 53

Systems, Man & Cybernetics - April 2017 - 54

Systems, Man & Cybernetics - April 2017 - 55

Systems, Man & Cybernetics - April 2017 - 56

Systems, Man & Cybernetics - April 2017 - Cover3

Systems, Man & Cybernetics - April 2017 - Cover4


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