AN EFFICIENT AND EFFECTIVE IMAGE SEGMENTATION

INTERACTIVE TOOL

Dorit S. Hochbaum

UC Berkeley Ca 94720, U.S.A.

Keywords:

Array-CGH, Comparative Genomics, Arabidopsis Ecotypes, Hidden Markov Model(HMM).

Abstract:

This paper describes a utilization of a very efﬁcient polynomial time algorithm, discovered by Hochbaum

(2001), for segmentation tool through Markov Random Fields. The tool allows ﬂexible choice of input param-

eters, controlling the output within an interactive tool with dynamic features and easily modiﬁed parameters.

1 INTRODUCTION

Image segmentation is one of the most fundamental

and challenging problems in computer vision with ap-

plications, such as pattern recognition, object detec-

tion, and medical imaging. The procedures engaged

for solving many of the segmentation problems with

large size data sets, apply heuristics and approxima-

tions techniques, which use approaches such as aggre-

gation, preprocessing with clustering, sampling, spec-

tral analysis or decomposition. These methods are

limited by the quality of the heuristics and are compu-

tationally too expensive to be used in many practical

images and certainly not in interactive settings.

In many image segmentation problems, a human

user can easily see the segments, patterns and fea-

tures. This human ability has occasionally been re-

cruited to aid segmentation. Here we are concerned

with images where a human user cannot differentiate

important and salient features. Instead, the segmen-

tation algorithm is used to bring forth these features

and very efﬁciently.

This paper presents an efﬁcient segmentation

method and its interactive use in order to detect fea-

tures that are not visible to a human user in the noisy

input image. As such it is capable of identifying tu-

mors and other pathologies in noisy medical images,

or in images where an adversary is hiding certain ob-

jects. The tool presented is tested on brain images

(Collins et al., 1998). We show that lesions that are

difﬁcult to detect in the input image can be identiﬁed

with the use of the methodology proposed here.

2 THE METHODOLOGY

A noisy or corrupted image is characterized by lack-

ing uniform color areas, which are assumed to charac-

terize a true image. To achieve higher degree of uni-

form color areas, it is reasonable to assign a penalty

to neighboringpixels that have differentcolors associ-

ated with them. On the other hand, the purpose of the

segmentation is to represent the “true” image. For that

purpose the given assignment of colors in the input

image is considered to be the “priors” on the colors of

the pixels, and as such, the best estimate available on

their true labels. Therefore, any change in those pri-

ors is assigned a penalty for deviating from the priors.

The Markov Random Fields optimization prob-

lem for the image segmentation problem is to assign

colors to each pixel so that the total penalty is min-

imized. The penalty consists of two terms. One is

the separation penalty term and the second is the de-

viation penalty term. For this reason we refer to this

penalty minimization problem also as the separation-

deviation problem (SD). This problem has been ex-

tensively studied over the past two decades, see e.g.

(Geiger and Girosi, 1991; Geman and Geman, 1984).

In the formulation of the MRF problem the input im-

age has each pixel in the pixel set P associated with

a color in a given set X = {1, . . . , k}. The neighbor-

hood of pixel i, which contains pixels adjacent to i, is

denoted by N(i). We wish to assign each pixel i ∈ P

an intensity x

∈ X so that the sum over all pixels of

the deviation cost G

(·) and the separation cost F

(·)

is minimized:

(SD) minD

∑

j∈V

− x

) + S

∑

(i, j)∈N(i)

− x

subject to x

∈ X for i ∈ V ,

459

Hochbaum D. (2009).

AN EFFICIENT AND EFFECTIVE IMAGE SEGMENTATION INTERACTIVE TOOL.

In Proceedings of the International Conference on Bio-inspired Systems and Signal Processing, pages 459-461

DOI: 10.5220/0001379304590461

 SciTePress

where the deviation function depends on the devia-

tion of the assigned color from the given intensity, r

and the separation is a function of the difference in as-

signed intensities between adjacent pixels (x

and x

D and S are constant integers multiplying the devia-

tion and separation terms respectively. If S = 0 then

the output is the same as the input, if the colors of

the input are in X, otherwise each pixel is assigned a

”nearest” color label in X. If D = 0 then the output is

a single color label assigned to all nodes. The values

of S and D, if positive, are not important. Only the

ratio of

is important in determining the degree of

color uniformity in the image. The larger this ratio,

the greater the color uniformity.

The complexity of the separation-deviation prob-

lem depends on the form of the penalty functions. A

full classiﬁcation of the problem’s complexity is given

in (Hochbaum, 2001) showing that for convex penalty

functions the problem is polynomially solvable, and

for non-convex the problem is NP-hard. The cases

when the deviation penalty functions are convex and

the separation penalty functionsare linear, for positive

and negative deviations (e.g. F

− x

) = |x

− x

|),

was shown by Hochbaum (Hochbaum, 2001) to be

solvable using an algorithm which is the fastest pos-

sible. For the type of problems we are interested in

the choice of linear separation functions gives better

results than convex quadratic ones.

3 THE INTERACTIVE TOOL

AND SOME RESULTS

The empirical implementation of the separation-

deviation algorithm is using a parametric minimum

s, t-cut algorithm code. Our code is based on the

pseudoﬂow algorithm of (Hochbaum, 2008) for max-

imum ﬂow and minimum cut. The code is accessi-

ble for download at (Chandran and Hochbaum, 2007).

Figure 1 shows the synthetic noisy image, which was

used as the input in this illustration and its corre-

sponding true brain image, (Collins et al., 1998).

Noisy Image

True Image

Figure 1: Brain image, Noisy and True.

The current algorithm’s interface tool supports the

following interactive functions:

Segment Image with a Fixed Number of Automat-

ically Selected Colors. For a selected number of

colors the tool uses a k-means algorithm to select the

colors. The number of colors is not necessarily equal

to the number of segments as each color set is not re-

stricted to be a connected component.

Segment for a Speciﬁc Selected Color Set X. The

user can add or remove colors from an existing color

set by clicking on any pixel in the image, or manually

insert the color code. As derived from the theory (out-

lined in an expanded version of this paper), the output

image can be generated by reading the existing output

and without additional computation.

Uniform Increase/Decrease in Deviation and Sep-

aration Costs. The tools allows to modify the ratio

. The effect of modifying this ratio is illustrated in

Figure 2 for the brain images, shown in Figure 1. In

that image here are four small lesions. We then apply

the separation-deviation algorithm with D = 2 and for

increasing values of S. The lesions show very clearly

in the high separation images.

S = 30

S = 40

S = 50

S = 60

S = 70

S = 80

Figure 2: The output for increasing values of S when ap-

plied to noisy brain image.

Color Restricted Change in Deviation. When the

user suspects that a certain color area may indicate an

object of interest, it is possible to increase the devi-

ation functions associated with this color only. So

for selected color g the deviation function G

, g)

is increased by the selected factor for all pixels with

input color g. This guarantees that any pixel with

input color equal to g is more likely to show in

the segmented output, even though it is small and

has unusual boundaries that otherwise would have

been “cleaned” by the separation penalty dominance.

When selecting, for example, in the brain image in

Figure 1, the color orange, it appears as the color of 3

out of the 4 lesions, as can be seen in Figure 3. When

the deviation for that color is increased the lesions

BIOSIGNALS 2009 - International Conference on Bio-inspired Systems and Signal Processing

460

become better segmented and more prominent. Of

course, the color orange also appears in other areas of

the brain shell where it is of no clinical signiﬁcance.

This issue will be addressed in the next prototype of

the interactive tool, where the deviation increase will

apply only in a user-deﬁned window.

Effect of increasing Deviation penalty for selected

color (orange )

k = 5, D = 2, S = 70

Figure 3: Increased deviation penalty for a selected color in

brain image.

Choose Neighborhood Adjacency. Neighborhood

is commonly referred to 8-or a 4-neighbor adjacency.

The algorithm is independent of planarity or any other

graph properties. The neighborhood thus is not re-

stricted to the 4-neighbor setup that is the most com-

mon in other image segmentation algorithms. Any

other type of neighborhood can be used, but an inter-

face creating the corresponding graph is required.

4 CONCLUSIONS

We demonstrate here that the interactive tool seg-

ments successfully the salient features in true images,

and can identify hidden important features and han-

dle efﬁciently noisy images. As such the separation

deviation interactive tool and algorithm is a useful ad-

dition to a segmentation tool box which considerably

enhances current capabilities.

ACKNOWLEDGEMENTS

The author’s research has been supported in part by

CBET-0736232 and NSF award No. DMI-0620677.

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