3D Adaptive Histogram Equalization Method for Medical Volumes

Paulo Amorim

, Thiago Moraes

, Jorge Silva

and Helio Pedrini

Division of 3D Technologies, Center for Information Technology Renato Archer, Campinas-SP, 13069-901, Brazil

Institute of Computing, University of Campinas, Campinas, SP, 13083-852, Brazil

Keywords:

Contrast Enhancement, Medical Images, Histogram Equalization, Volume Rendering.

Abstract:

Medical imaging plays a fundamental role in the diagnosis and treatment of several diseases, enabling the

visualization of internal organs and tissues for use in clinical procedures. The quality of medical images can

be degraded by several factors, such as noise and poor contrast. The application of ﬁltering and contrast en-

hancement techniques is usually necessary to improve the quality of images, which facilitates the segmentation

and classiﬁcation stages. In this paper, we develop and analyze a novel three-dimensional adaptive histogram

equalization method for improving contrast in the context of medical imaging. Several data sets are used to

demonstrate the effectiveness of the proposed approach.

1 INTRODUCTION

Several medical imaging modalities (Ahmad et al.,

2014; Beutel et al., 2000) have been employed in

modern medicine to aid the diagnosis and treat-

ment of diseases, such as digital radiography (DR),

magnetic resonance imaging (MRI), endoscopy (ES),

ultrasound (US), angiography (AG), mammography

(MG), computed tomography (CT) and positron emis-

sion tomography (PET). These imaging techniques al-

low visual representations of internal structures of the

body to be constructed, assisting physicians in diag-

nostic decisions (Nolden et al., 2013; Thammasitboon

and Cutrer, 2013).

During the acquisition process, the quality of

medical images can be degraded by artifacts, for in-

stance, noise and poor contrast. Techniques of im-

age ﬁltering and contrast enhancement are necessary

to compensate such effects in order to improve the

image quality.

In the image processing ﬁeld (Amorim et al.,

2013; Amorim et al., 2015; Moraes et al., 2015),

several approaches have been developed to attenuate

noise while preserving relevant features. Some com-

mon noise removal approaches (Gonzalez and Woods,

2002; Parker, 2010; Russ, 2015) include median ﬁlter,

Weiner ﬁlter, Gaussian ﬁlter, bilateral ﬁlter, among

others. Additionally, enhancement techniques (Hum-

mel, 1977; Singh and Bovis, 2005; Stark, 2000) have

been employed to emphasize features or characteris-

tics of the image, such that the resulting image has

superior quality than the original one.

Histogram equalization (Gonzalez and Woods,

2002; Hummel, 1977) is a very well known tech-

nique for enhancing the contrast of an image, whose

main goal is to better distribute the pixel intensities

based on the probability distribution of the gray lev-

els. By means of this histogram adjustment, regions

with poor contrast are enhanced, producing an overall

contrast improvement.

As main contribution of our work, we propose

and evaluate a variant of the two-dimensional con-

trast limited adaptive histogram equalization (2D

CLAHE) (Zuiderveld, 1994) to improve contrast in

medical images. It differs from the original approach

in the sense that our method operates directly on the

three-dimensional volumes, without requiring the ex-

traction of two-dimensional sections of images.

Several histograms are constructed and modiﬁed

to redistribute the pixel intensities of the images, sig-

niﬁcantly improving their local contrast. Experiments

are conducted on different medical volumetric data

sets to demonstrate the effectiveness of the proposed

method.

This paper is organized as follows. Section 2

brieﬂy reviews some relevant concepts and techniques

related to the topic under investigation. Section 3

describes the proposed local contrast enhancement

method. Section 4 presents and analyzes the exper-

imental results obtained with our method. Section 5

concludes the paper with some ﬁnal remarks and di-

rections for future work.

Amorim, P., Moraes, T., Silva, J. and Pedrini, H.

3D Adaptive Histogram Equalization Method for Medical Volumes.

DOI: 10.5220/0006615303630370

In Proceedings of the 13th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2018) - Volume 4: VISAPP, pages

363-370

ISBN: 978-989-758-290-5

363

2 BACKGROUND

A common problem that occurs in medical imaging is

the generation of images with poor contrast due to a

limited exposure range, which affects the correct in-

terpretation of anatomical structures for diagnosis and

treatment procedures.

Enhancement techniques (Chen et al., 2014; Gu

et al., 2016; Huang et al., 2013; Kim et al., 1998;

Saleem et al., 2017; Stark, 2000; Wang et al., 1983)

have been developed to adjust the contrast and im-

prove quality of images in order to make their char-

acteristics more suitable for subsequent stages, such

as segmentation and classiﬁcation. Therefore, after

the image enhancement process of an image, a cer-

tain component becomes more distinguishable from

other components and the background.

Several deﬁnitions of contrast have been proposed

in the literature. Weber contrast (Fechner, 1860) is

expressed as:

I − I

(1)

where I and I

correspond to the luminance of the ob-

jects and the background, respectively.

Michelson contrast (Michelson, 1995) is deﬁned

as:

max

− I

min

max

+ I

min

(2)

where I

min

and I

max

correspond to the lowest and high-

est luminance, respectively.

Root mean square (RMS) contrast (Peli, 1990) is

deﬁned as the standard deviation of the pixel intensi-

ties:

RMS

M−1

∑

x=0

N−1

∑

y=0

−

(3)

where I

are the elements with x and y coordinates of

the image with dimensions M × N, whereas

I is the

average intensity of all pixel intensities in the image.

The pixel intensities of I are normalized in the range

[0,1].

Contrast stretching (Arici et al., 2009; Chang and

Wu, 1998; Yang, 2006) is a basic image enhancement

technique used to increase the dynamic range of the

gray levels present in the image. A low contrast im-

age typically has its pixel intensities concentrated on

a narrow range, such that information may be lost.

Linear contrast enhancement techniques expand

the original intensity values of the pixels linearly.

Three linear contrast enhancement techniques are

brieﬂy described as follows. In the minimum-

maximum linear contrast stretching, the pixel values

are redistributed to a new range of values speciﬁed

by lower and upper pixel value limits over the im-

age under normalization. For 8-bit gray level im-

ages, the lower and upper limits are usually assigned

to 0 and 255, respectively. In the percentage linear

contrast stretching, the enhancement is similar to the

minimum-maximum approach, however, it employs

speciﬁed minimum and maximum values within a cer-

tain percentage of pixels from the mean of the his-

togram. In a piecewise linear contrast stretching, the

range of the image intensity is expanded in selected

areas according to linear function.

Nonlinear contrast enhancement techniques apply

non-linear transfer functions to redistribute the inten-

sity values of pixels to increase the contrast of an

image. Histogram equalization applies a monotonic

non-linear mapping to adjust the intensity values of

pixel in the image such that the resulting image con-

tains a uniform distribution of intensities. The cumu-

lative probability distribution can be used to equalize

the histogram of an image.

The histogram equalization (Abdullah-Al-Wadud

et al., 2007; Cheng and Shi, 2004; Gonzalez and

Woods, 2002; Pizer et al., 1987; Russ, 2015) is typ-

ically a global process in the sense that it applies a

function to transform the image based on the inten-

sity level distribution of the entire image. In certain

cases, it is desirable to enhance details over small re-

gions of the image, such that the equalization process

can be adapted to produce a local enhancement. In

adaptive histogram equalization, the image is divided

into a number of non-overlapping blocks, such that

the histogram equalization mapping is applied locally

within each block. In order to remove artifacts due to

block boundaries, the pixel intensities are interpolated

across the blocks using an interpolating function.

A variant of the adaptive histogram equal-

ization, known as contrast limited adaptive his-

togram equalization (2D CLAHE), was proposed by

Zuiderveld (Zuiderveld, 1994) to avoid noise to be

overampliﬁed in homogeneous regions of the image.

This approach limits noise ampliﬁcation by clipping

the histogram through a speciﬁed value before com-

puting the cumulative distribution function. Instead

of discarding the part of the histogram that exceeds

the clip limit, it is redistributed uniformly among all

histogram bins (Pizer et al., 1987).

3 PROPOSED METHOD

This section describes the main stages that compose

the proposed method for locally equalizing the his-

togram of the medical images. The method oper-

ates directly on the three-dimensional volumes, which

VISAPP 2018 - International Conference on Computer Vision Theory and Applications

364

is an extension of the contrast limited adaptive his-

togram equalization (2D CLAHE) (Zuiderveld, 1994)

to improve contrast in medical images. Figure 1

illustrates the main components of the proposed

three-dimensional contrast limited adaptive histogram

equalization (3D CLAHE).

Initially, two-dimensional slices are stacked to-

gether to form a volume. The volume is then subdi-

vided in blocks with predeﬁned size. The histogram is

calculated for each block and part of histogram is cut

according to a predeﬁned value. Finally, the blocks

are joined and a trilinear interpolation function is ap-

plied to remove artifacts that may occur on the bound-

aries between blocks.

Algorithm 1 describes the main steps of the

proposed three-dimensional contrast limited adap-

tive histogram equalization (3D CLAHE). Function

CDF denotes the Cumulative Distribution Function,

whereas functions min and max return the minimum

and maximum grayscale values in the given image,

respectively. H is a vector of histograms, where each

position of the vector stores the histogram of a sub-

block, CS is an auxiliary vector to store the result of

CDF, and MAP is a vector that maps each grayscale

value to a new intensity value after the histogram

equalization.

The trilinear interpolation is expressed as

[(MAP

LUA

] × x_inv_coe f × y_inv_coe f × z_inv_coe f )+

(MAP

RUA

] × x_coe f × y_inv_coe f × z_inv_coe f )+

(MAP

LBA

] × x_inv_coe f × y_coe f × z_inv_coe f )+

(MAP

LU P

] × x_inv_coe f × y_inv_coe f × z_coe f )+

(MAP

RU P

] × x_coe f × y_inv_coe f × z_coe f )+

(MAP

LBP

] × x_inv_coe f × y_coe f × z_coe f )+

(MAP

RBA

] × x_coe f × y_coe f × z_inv_coe f )+

(MAP

RBP

] × x_coe f × y_coe f × z_coe f )]

/(size

× size

)

where MAP

LUA

, MAP

RUA

, MAP

LBA

, MAP

LUP

MAP

RUP

, MAP

LBP

, MAP

RBA

, MAP

RBP

are the maps

for the 8 nearest subblocks (Figure 2). x_coe f ,

y_coe f , z_coe f are the distances from V

to MAP

LBA

for x, y and z, respectively. x_inv_coe f , y_inv_coe f ,

z_inv_coe f is the distance from V

to MAP

RU P

for x,

y and z, respectively.

To test our contrast enhancement methodology,

we employed MRI volumes, which were subdivided

into blocks with size of 8×8×8 voxels. Larger block

dimensions, such as 16×16×16 voxels, generated

much noise and decreased the peak signal noise ratio

(PSNR) values.

The histogram clip value used in our methodology

was assigned to 5, since larger values also increased

the noise level in the image, consequently decreasing

the PSNR value.

Algorithm 1: Proposed 3D CLAHE method.

1 3D_CLAHE (image, size, clip_limit, nbins)

input : image: volumetric image;

size: size of subblocks;

clip_limit: value at which the

histogram is clipped;

nbins: number of bins for

histogram;

output: image_equalized;

2 Divide image into subblocks with the given

size;

3 Create image_equalized with same size as

image;

4 for each subblock S

5 H[S

] ← histogram(S

, nbins);

6 Clip H[S

] according to clip_limit and

redistribute equally the excess voxels

across the histogram;

7 CS ← CDF(H[S

]);

8 MAP[S

] ← CS × (max(image) -

min(image)) + min(image);

9 for each voxel V

from image do

10 Find 8 closest neighboring subblocks

centers;

11 Use the pixel intensity to ﬁnd the map

value at the 8 subblocks;

12 Use the 8 mapped values to interpolate

with trilinear interpolation to obtain

the V

mapped value and assign this

value to the corresponding voxel in

image_equalized;

13 return image_equalized;

4 EXPERIMENTAL RESULTS

Experiments were conducted on a set of ﬁve volumes

acquired through magnetic resonance imaging (MRI).

These images were extracted from the publicly avail-

able OASIS dataset (Marcus et al., 2007).

Magnetic resonance imaging was chosen since

this modality commonly generates images with het-

erogeneous contrast when compared to computed to-

mography (CT). Each volume contains 256 slices at a

resolution of 128×256 pixels.

We compared the proposed method (3D CLAHE)

against 2D CLAHE (Zuiderveld, 1994). For 2D

CLAHE, the equalization was applied to each slice

of the volume using blocks with 8 × 8 pixels. For 3D

3D Adaptive Histogram Equalization Method for Medical Volumes

365

Figure 1: Proposed methodology for three-dimensional contrast limited adaptive histogram equalization.

MAP

LBP

MAP

LUA

MAP

RUA

MAP

LUP

MAP

RUP

MAP

RBA

MAP

RBP

MAP

LBA

Figure 2: Centers of the 8 subblocks form a cube, which illustrates the position of the maps used in the interpolation.

CLAHE, we used blocks with 8× 8 × 8 voxels. A his-

togram clip limit of 5 was used in both approaches.

In the ﬁrst row of Figures 3 and 4, all images are

non-equalized. It is possible to observe that these im-

ages have different level of contrast. Images in the

second row were equalized with the 2D CLAHE tech-

nique. They present better contrast when compared

to their corresponding original images, however, the

have different contrast between the slices which it is

not ideal for volume rendering or 3D segmentation

purpose. Finally, images in the third row of Figures 3

and 4 were equalized with the proposed 3D CLAHE

method, which present uniform contrast.

The peak signal noise ratio (PSNR) was measured

for both 2D CLAHE and 3D CLAHE methods. It

is possible to observe from Table 1 that our method

achieved higher values of PSNR for all tested images,

which means that they are closer to the original im-

age.

Figure 5 shows the results of volume rendering

with raycasting technique for two volumes equalized

with 2D CLAHE and with the proposed technique.

The details in the surface of the brain are clearly vis-

ible when the volumetric data sets are equalized with

the proposed method.

VISAPP 2018 - International Conference on Computer Vision Theory and Applications

366

original

slice 179

original

slice 180

original

slice 181

slice 179

equalized with 2D CLAHE

slice 180

equalized with 2D CLAHE

slice 181

equalized with 2D CLAHE

slice 179

equalized with 3D CLAHE

slice 180

equalized with 3D CLAHE

slice 181

equalized with 3D CLAHE

Figure 3: Comparison between input and equalized images with 2D CLAHE and proposed 3D CLAHE method.

3D Adaptive Histogram Equalization Method for Medical Volumes

367

original

slice 84

original

slice 85

original

slice 86

slice 84

equalized with 2D CLAHE

slice 85

equalized with 2D CLAHE

slice 86

equalized with 2D CLAHE

slice 84

equalized with 3D CLAHE

slice 85

equalized with 3D CLAHE

slice 86

equalized with 3D CLAHE

Figure 4: Comparison between input and equalized images with 2D CLAHE and proposed 3D CLAHE method.

Table 1: PSNR values for equalized volumes with 2D CLAHE and proposed method.

Dataset PSNR

2D CLAHE 3D CLAHE

OAS2_0001_MR1_RAW_mpr-1.nifti.hdr 21.01 73.98

OAS2_0002_MR1_RAW_mpr-1.nifti.hdr 22.24 66.31

OAS2_0003_MR1_RAW_mpr-1.nifti.hdr 18.63 66.86

OAS2_0004_MR1_RAW_mpr-1.nifti.hdr 25.08 68.58

OAS2_0005_MR1_RAW_mpr-1.nifti.hdr 29.01 30.13

VISAPP 2018 - International Conference on Computer Vision Theory and Applications

368

equalized with 2D CLAHE equalized with proposed method

Figure 5: Comparison between two volumetric data sets equalized with 2D CLAHE and proposed method.

5 CONCLUSIONS AND FUTURE

WORK

In this paper, we extended the contrast limited adap-

tive histogram equalization technique for improving

contrast in medical images. Differently from the

original method, our method operates directly on

the three-dimensional MRI volumes, where the his-

tograms are computed and transformed within blocks

extracted from the medical data.

Experiments conducted on a number of medical

volumes demonstrated that the proposed method was

capable of signiﬁcantly enhancing the contrast of the

images. The resulting volumes can provide health

professionals with valuable information for diagnosis

and treatment purposes.

As directions for future work, we intend to inves-

tigate the extension of other 2D image enhacement

techniques to 3D.

ACKNOWLEDGMENTS

We are grateful to Brazilian Council for Scien-

tiﬁc and Technological Development (CNPq) for

Grant #305169/2015-7 and to São Paulo Research

Foundation (FAPESP) for the Brazilian Research

Institute for Neuroscience and Neurotechnology -

BRAINN (CEPID process #2013/07559-3) and for

the Thematic Projects (Grants #2017/12646-3 and

#2014/12236-1).

3D Adaptive Histogram Equalization Method for Medical Volumes

369

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