BINARIZATION OF PHASE CONTRAST VOLUME IMAGES OF

FIBROUS MATERIALS

A Case Study

Filip Malmberg

Centre for Image Analysis, Uppsala University, Uppsala, Sweden

Catherine

Ostlund

STFI-Packforsk AB, Stockholm, Sweden

Gunilla Borgefors

Centre for Image Analysis, Swedish University of Agriculture, Uppsala, Sweden

Keywords:

X-ray microtomography, Graph cut segmentation, Phase Contrast, Fibrous materials.

Abstract:

In this paper, we present a method for segmenting phase contrast volume images of ﬁbrous materials into

ﬁbre and background. The method is based on graph cut segmentation, and is tested on high resolution X-ray

microtomography volume images of wood ﬁbres in paper an composites. The new method produces better

results than a standard method based on edge-preserving smoothing and hysteresis thresholding. The most

important improvement is that the proposed method handles thick and collapsed ﬁbres more accurately than

previous methods.

1 INTRODUCTION

1.1 Background

Wood ﬁbres are used in many types of materials. The

most common such materials are paper and board,

which consist of a dense network of pulp ﬁbres. An-

other, quite new application for wood ﬁbres is com-

posite materials, where a network of pulp ﬁbres is

used to reinforce a plastic matrix.

Recently, X-ray microtomography has been suc-

cessfully used to capture high resolution volume im-

ages of ﬁbrous materials non-destructively (Antoine

et al., 2002; Samuelsen et al., 2001). Automated anal-

ysis of such images can give a lot of useful informa-

tion about the properties of the material.

As described in (Samuelsen et al., 2001), the most

straightforward way of providing the contrast neces-

sary for imaging with X-rays is to use beam absorp-

tion. However, when imaging low-density materials,

such as pulp ﬁbres, it is difﬁcult to get enough con-

trast using absorption. For such materials, phase con-

trast can be used instead. In phase contrast images,

changes in refractive index of the imaged sample, i.e.,

the interfaces between different materials in the sam-

ple, are detected. In phase contrast volume images

of ﬁbrous materials, the interface between ﬁbre and

background is visible as a bright band on the ﬁbre side

of the interface and a dark band on the background

side. These dark and bright bands will be denoted in-

terface bands. A small part of a slice from a volume

that exhibits these phenomena is shown in Figure 1.

Both absorption contrast and phase contrast ef-

fects may be present in an image. With X-ray micro-

tomography, the balance between absorption contrast

and phase contrast is determined by the distance be-

tween the sample and the imaging sensor.

Since many image analysis methods require a bi-

nary image as input, segmenting the images into ﬁbre

and background is an important pre-processing step.

We call this step binarization. The balance between

phase contrast and absorption contrast in the image

affects the choice of binarization method.

In absorption images, the intensity of each image

element corresponds to the density of the material it

148

Malmberg F., Ã

Ustlund C. and Borgefors G.

BINARIZATION OF PHASE CONTRAST VOLUME IMAGES OF FIBROUS MATERIALS - A Case Study.

DOI: 10.5220/0001781301480153

In Proceedings of the Fourth International Conference on Computer Vision Theory and Applications (VISIGRAPP 2009), page

ISBN: 978-989-8111-69-2

Bright band

Dark band

Figure 1: Part of a slice from a pulp-ﬁbre composite sample

imaged with phase contrast X-ray microtomography. Bright

and dark interface bands are visible at the boundaries be-

tween ﬁbre and background.

represents. Given that there are sufﬁcient differences

in density between the imaged materials, the intensity

of an element directly indicates which material it be-

longs to. Thus the image can, in theory, be segmented

by thresholding the intensity values. In practice, the

image is often corrupted by noise and other artifacts,

that must be removed or reduced before thresholding

can be applied.

Phase contrast images are conceptually harder to

binarize than absorption images, since most indi-

vidual image elements contain no information about

which material they belong to. Instead, we only have

information about the boundaries between the dif-

ferent materials. At these boundaries, however, in-

terface bands provide local information about which

side of the boundary that corresponds to which ma-

terial. To binarize the image, this local information

must somehow be propagated to the rest of the im-

age in a consistent way. Here, we present a method

for binarizing phase contrast volume images contain-

ing two distinct materials. The method ﬁrst identiﬁes

the interface bands using thresholding. These are then

used as input for segmentation with minimal graph

cuts (Boykov, 2006).

1.2 Previous Work

Binarization of absorption mode volume images of ﬁ-

brous materials has been addressed in a number of pa-

pers during recent years. The most common approach

is to use some kind of edge preserving smoothing to

reduce image noise. The ﬁltered image is then bina-

rized using thresholding or region growing. Isolated

structures that are considered too small to be ﬁbres are

then removed using morphological operations. Vari-

ants of this approach were used in, e.g., (du Roscoat

et al., 2005), (Bache-Wiig and Henden, 2005) and

(Martin-Herrero and Germain, 2007).

In the phase-contrast images shown here, the

width of the interface bands are about the same as

the width of the ﬁbre walls. The interior of many ﬁ-

bres are therefore ﬁlled entirely by the bright inter-

face band. This means that many ﬁbres are brighter

than the background. Therefore, it is tempting to

use a threshold-based method for binarization. How-

ever, this approach will make it hard to correctly bi-

narize collapsed ﬁbres and ﬁbres with thicker walls,

since the interior of these ﬁbres will have about the

same intensity level as the background. Using edge-

preserving ﬁlters, it may be possible to propagate the

intensity values of the bright interface band to the in-

terior of such ﬁbres, although this might require very

precise parameter settings and the results will be hard

to predict.

A method for segmenting phase contrast images

of carbon-carbon composites is presented in (Vig-

noles, 2001). Two thresholds, one high and one low,

are applied to the image to identify the bright and dark

interface bands respectively. An intermediate image

is then constructed where the identiﬁed bright inter-

face bands are set to white, the identiﬁed dark inter-

face bands are set to black, and all other image ele-

ments are set to gray. We will call this type of inter-

mediate image a trimap.

Two different methods for reconstructing the seg-

mented image from the trimap are described in (Vig-

noles, 2001). In the ﬁrst method, the boundary of each

connected gray region is examined. If the boundary is

predominantly white, the region is labeled as white,

and vice versa. This method is based on the assump-

tion that there are no holes in the interface bands. This

assumption is often violated in real images, due to

noise and other artifacts, and in such cases the method

may fail drastically.

In the second method, all gray elements that have

at least one non-gray neighbor are examined. If the

element has more white neighbors than black neigh-

bors, it is set to white. Else it is set to black. This pro-

cedure is repeated until no gray elements remain. This

method is more robust to “leaks” in the bands than the

ﬁrst method. However, only the binary information

from the identiﬁed interface bands is used to delin-

eate the boundaries in the image. In regions where

the interface bands are too weak to be correctly iden-

tiﬁed by thresholding, no image information is used

in the delineation of the ﬁbre boundary.

1.3 Outline of the Proposed Method

The method proposed in this paper is conceptually

similar to the methods in (Vignoles, 2001). Just as

BINARIZATION OF PHASE CONTRAST VOLUME IMAGES OF FIBROUS MATERIALS - A Case Study

149

in that paper, a trimap, where each element is labeled

as either ﬁbre, background or unknown, is created.

We will, however, use minimal graph cuts to create

a binary image from the trimap. Segmentation with

graph cuts will be explained in detail in the next sec-

tion. Using graph cuts has the advantage that image

information can be taken into account even in areas

where the interface bands are too weak to be detected

by thresholding.

2 GRAPH CUT SEGMENTATION

Graph cut segmentation is an image segmentation

method based on combinatorial optimization tech-

niques. The method is applicable to images of any

dimension and gives a binary partitioning of the im-

age into background and object.

In graph cut segmentation the image is interpreted

as a graph, where image elements correspond to nodes

and paths between adjacent elements correspond to

graph edges. Each graph edge is assigned a non-

negative cost. Two special nodes are added to the

graph, the source node and the sink node. Image el-

ements that are a priori known to belong to the ob-

ject are connected to the source node with zero cost

edges. Similarly, elements that are known to belong

to the background are connected to the sink node. A

cut on the a graph is a set of edges that, if removed

from the graph, separate the source from the sink. A

cut thus associates each node with either the source

or the sink. The cost of a cut is the sum of the cost

of all edges in the cut, and a minimal cut is a cut such

that no other cut has a lower cost. A computationally

efﬁcient algorithm for computing minimal graph cuts

was described in (Boykov and Kolmogorov, 2004).

The fundamental idea of graph cut segmentation

is that a minimal cut on the graph of an image corre-

sponds to an optimal partitioning of the image into

background and object, subject to the constraints

given by the edge weights and the geometry of the

graph. An illustration of this concept is shown in Fig-

ure 2.

From a user perspective, this means that we must

supply a trimap image, where each element is labeled

as either background, object or unknown. Further-

more we must supply a costmap image, where the

value of each element is inversely proportional to the

“likelihood” that the element belongs to the bound-

ary of the object of interest. This is typically based

on image features that describe strong edges in the

image, such as the gradient magnitude of the image.

The graph cut method then produces a binary segmen-

tation, where the boundary between the object and the

Figure 2: Principle of graph cut segmentation. Left: Initial

state of the graph. Right: A cut on the graph.

background is located at strong edges in the image.

3 METHOD

In order to apply graph cut segmentation to phase

contrast images, we need to create a trimap and a

costmap. The trimap is created using essentially the

same approach as that in (Vignoles, 2001). The vol-

ume is thresholded at two values, one low value and

one high value. This produces two binary images that

represent the dark and bright interface bands, respec-

tively.

For images with strong noise, good threshold val-

ues may not exist. In such cases we have used hystere-

sis thresholding (Canny, 1986) to identify the inter-

face bands. The user must thus specify two threshold

values, t

1,1

and t

1,2

, for segmenting the bright inter-

face bands, and two threshold values, t

2,1

and t

2,2

, for

segmenting the dark interface bands.

The two binary images containing the interface

bands are then merged into a single trimap. The

trimap does not have to be complete, i.e., leaks in

the interface bands are allowed. However, elements

wrongly labeled as ﬁbre or background should be

avoided, since any such errors will remain in the ﬁ-

nal binarization.

Since the graph cut algorithm is computationally

expensive, it is desirable to keep the number of nodes

in the graph as small as possible. In practice, only

the unknown elements are included in the graph. Re-

ducing the number of unknown elements in the trimap

thus reduces the computation time.

In order to exclude uninteresting elements (i.e. el-

ements that are highly unlikely to belong to a ﬁbre)

from the computations we have used the following

heuristic: A 3D distance transform (Borgefors, 1996)

is computed from the bright image elements, i.e. ele-

ments known to be inside the ﬁbres. The distance map

is truncated at some distance value, and elements with

larger distance values are labeled as background. The

threshold value should be as small as possible in or-

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150

Figure 3: The different steps of the proposed method. Top left: A slice from the original volume. Top right: Costmap. Bottom

left: Trimap. Bottom right: Binarization result after graph cut segmentation and removal of small isolated structures.

der to minimize the computation time, but still large

enough not to discard any ﬁbre elements. We have

found during our experiments that suitable values for

a batch of images are not hard to ﬁnd manually by

visual inspection.

The costmap c is computed using 3D Sobel ﬁlters.

Edge responses dx, dy and dz are computed separately

along the three coordinate axes of the volume. The

following convolution ﬁlter is used in each direction:





1 0 −1

2 0 −2

1 0 −1





The magnitude of the gradient vector formed by

these three components is then used as a cost function:

c =

+ dy

+ dz

(1)

Once the trimap and the costmap are created,

graphcut segmentation is applied.

If the trimap contains some false ﬁbre regions due

to noise in the image, this might result in small iso-

lated ﬁbre regions in the binarized image. As an op-

tional post-processing step, isolated regions smaller

than some speciﬁed size (e.g., a few elements) may

be removed using morphological operations (Sonka

et al., 1998). The different steps of the method are

shown in Figure 3.

4 EXPERIMENTS

Volume images of ﬁbrous materials (paper, board,

pulp-ﬁbre composites) were captured with X-ray

microtomography at the European Synchrotron Ra-

diation Facility (ESRF) in Grenoble, at the ID19

beam line. The size of each reconstructed volume

is 2048x2048x1280 voxels, with gray-values in the

range [0,255]. The voxels are isotropic, with a side

length of approximately 0.7µm. Ring artifacts present

in the images were reduced using the method de-

scribed in (Axelsson et al., 2006).

The volumes were binarized using the proposed

method. In order to reduce computation time, each

volume was divided into subvolumes (512x512x256),

and graph cut segmentation was applied separately to

each of the subvolumes. This procedure might pos-

sibly introduce some errors at the borders of the sub-

volumes. However, we were unable to detect any such

errors during visual inspection of the merged results.

Parameters for the construction of the trimaps

were determined through visual inspection, and the

same parameters were used for all subvolumes. A

software tool for quick visual inspection of volume

images, developed using The Visualization Toolkit

(VTK) (The Visualization Toolkit, 2008), was used

to make the evaluation easier. A screenshot from this

tool is shown in Figure 4. Table 1 shows the param-

eter settings for two different materials, a pulp-ﬁbre

composite and a newsprint paper.

For comparison purposes, the volumes were also

BINARIZATION OF PHASE CONTRAST VOLUME IMAGES OF FIBROUS MATERIALS - A Case Study

151

Figure 4: A screenshot from a tool, developed using VTK,

for quick visual inspection of volume images. The tool was

used to facilitate evaluation of parameter settings.

binarized using a threshold-based method. Follow-

ing the method described in (Bache-Wiig and Hen-

den, 2005), image noise was ﬁrst reduced using iter-

ated SUSAN-ﬁltering (Smith and Brady, 1997). The

ﬁltered volumes were then binarized using hysteresis

thresholding.

Table 1: Examples of parameter settings for trimap con-

struction.

Sample t

1,1

1,2

2,1

2,2

Pulp-ﬁbre composite 190 170 80 80

Newsprint paper 185 165 80 80

5 RESULTS

No ground truth segmentation exists for the studied

volumes, and therefore it is difﬁcult to make a quan-

titative comparison between the two tested methods.

Visual inspection of many segmented images, how-

ever, reveals some systematic differences. Both meth-

ods produce good segmentation results for thin, hol-

low ﬁbres. For collapsed and thick ﬁbres, however,

the threshold based method often fails to ﬁll the inte-

rior of the ﬁbre. As discussed in section 1.2, this is

due the fact that the SUSAN-ﬁltering fails to propa-

gate intensity values from the boundary of the ﬁbre far

enough into the interior regions. The proposed graph

cut based method, on the other hand, handles these

cases correctly. An example of this is shown in Fig-

ure 6. Surface renderings of two samples, binarized

using the proposed method, are shown in Figure 5.

The computation time for the proposed method is

Figure 5: Surface renderings of two samples, binarized us-

ing the proposed method. Top: Pulp-ﬁbre composite. Bot-

tom: Newsprint paper.

dominated by the graph cut segmentation. For each

subvolume, the graph cut segmentation was computed

in 3-4 minutes on a computer with eight 3GHz Intel

processors and 32 GB of RAM.

6 CONCLUSIONS

For X-ray microtomography images where the phase

contrast is stronger than the absorption contrast, the

proposed method gives better results than previous

methods based on the combination of edge-preserving

smoothing and thresholding.

The method might also be applied to other phase

contrast images. For the method to work, the images

should contain no more than two separate materials.

The refractive indices of the materials must be suf-

ﬁciently different, so that the interface bands at the

boundary between the materials can be identiﬁed with

thresholding.

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152

Figure 6: Comparison between threshold-based binarization and the proposed method. The red circles indicate a typical

example of a collapsed ﬁbre where the threshold-based method fails. Left: Original slice. Middle: The same slice, binarized

with iterated SUSAN-ﬁltering and hysteresis thresholding. Right: The same slice, binarized with the proposed method.

ACKNOWLEDGEMENTS

The European Synchrotron Radiation Facility (ESRF)

in Grenoble is gratefully acknowledged for the 3D im-

age data acquired during the Long Term project ME-

704, that was used in this study.

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