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3D volume segmentation is the process of partitioning voxels into 3D regions (subvolumes) that represent meaningful physical entities which are more meaningful and easier to analyze and usable in future applications. Multiresolution Analysis (MRA) enables the preservation of an image according to certain levels of resolution or blurring. Because of multiresolution quality, wavelets have been deployed in image compression, denoising, and classification. This paper focuses on the implementation of efficient medical volume segmentation techniques. Multiresolution analysis including 3D wavelet and ridgelet has been used for feature extraction which can be modeled using Hidden Markov Models (HMMs) to segment the volume slices. A comparison study has been carried out to evaluate 2D and 3D techniques which reveals that 3D methodologies can accurately detect the Region Of Interest (ROI). Automatic segmentation has been achieved using HMMs where the ROI is detected accurately but suffers a long computation time for its calculations.

Volume segmentation allocates the voxels in 3D images into partitions or 3D regions that represent meaningful physical entities. The goal is to distinguish between different regions in the 3D volume and cover the extracted contours from the entire volume. Voxels' classification into regions is performed according to a certain region to which the voxels belong, and some shared, predefined properties. Those voxels comprise an isolated or segmented Object Of Interest (OOI) from the input volume.

There are many existing techniques used for medical image segmentation, including Multiresolution Analysis (MRA), statistical methods, and thresholding- and clustering-based techniques. Clustering technique aims to classify each pixel in an image into the proper cluster, and then these clusters are mapped to display the segmented images. A certain clustering criterion can be adopted to group each pixel into a specific number of clusters depending on the image histogram [

MRA allows the preservation of an image according to certain levels of resolution. Consequently, wavelets have been useful in image compression, de-noising, and classification. Wavelet theory, which is built on solid mathematical foundations uses well-established tools such as quadrature mirror filtering, subband coding, and pyramidal image processing. Wavelet analysis enables the exploitation of signal or image characteristics associated with a particular resolution level, which may not be detected using other analysis techniques [

Statistical modeling is a set of mathematical equations which describes the behavior of an object of study in terms of random variables and the associated probability distribution. Markov Random Field Model (MRFM) is a statistical approach which has been utilized within segmentation methodologies to model spatial interactions between neighbor pixels [

Statistical models using Hidden Markov Models (HMMs) observe a sequence of emissions with a hidden sequence of states that the model went through to generate the emissions [

This paper focuses on the implementation of efficient and robust medical volume segmentation techniques. MRA including wavelet and ridgelet transforms have been deployed for feature extraction, while statistical modeling using HMMs has been used for segmentation. The outline of this paper is as follows. In the following section, the proposed segmentation system is illustrated and discussed. In Section

In medical applications, the source of the 3D data set is the acquisition systems such as Positron Emission Tomography (PET), Computerized Tomography (CT), or Magnetic Resonance Imaging (MRI). Such devices are capable of slicing an object in a physical sectioning. 3D data set from those devices can be considered as parallel slices stacked to form a 3D volume. A segmented medical volume into sub-volumes which are more meaningful and easier to analyze and understand is the output the proposed system illustrated in Figure

Proposed segmentation system.

Hybrid multiresolution statistical approaches and other segmentation techniques are used to achieve accurate segmented volumes. System input is a 3D phantom or real volume from scanner acquisition. Acquisition systems produce a number of 2D slices resulted from the scanned volume of the body. These slices can be individually segmented using 2D segmentation methods such as thresholding, clustering, and HMMs followed by volume reconstruction or directly using 3D segmentation methods such as 3D that thresholding or 3D discrete wavelet transform (3D-DWT) after volume reconstruction process.

This paper explains the new application of wavelet transform directly on the 3D medical volumes from the acquisition systems using 3D-DWT with Haar wavelet filter. HMMs have been also applied on those volumes slice-by-slice to segment the Region Of Interest (ROI) into a number of classes based on the grey scale values of the original volume pixels.

The mathematical background of the developed techniques for 3D medical volume segmentation system is presented in this section.

Scalar images can be segmented using thresholding approaches by partitioning image intensities. This methodology attempts to determine an intensity value that can separate the signal into a desired number of classes. Segmented images can be achieved by clustering all pixels with intensities larger than the threshold value into one class, and all others into another. In many applications, the threshold values selection can be done depending on the basis of histogram. Multithresholding occurs when more than one threshold value is determined [

The voxels of a certain object are not necessarily connected after thresholding because this technique does not consider the spatial characteristics of an image, thus causing it to be sensitive to noise and intensity fluctuations. For this reason it cannot be easily applied to many medical imaging modalities. These drawbacks essentially corrupt the histogram of the image-making partitioning via the selection of more problematic appropriate thresholds [

Hard thresholding technique is a boolean filter [

Hard thresholding process is less complex than soft thresholding (Algorithm

Thresholding technique for medical image segmentation at threshold value

It can be seen here that applying thresholding techniques is a very easy process and can be affected easily by surrounding noise, but it has been used as a preprocessing step and postprocessing step with other segmentation techniques. It is worth mentioning that thresholding can be replaced by the clustering technique which will be explained in Section

3D thresholding method is similar to the 2D approaches where thresholding process is applied on all pixels in the volume instead of that in the plane. Algorithm

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Clustering technique is the process of classifying each group of pixels in an image into one class, each class has the same or similar properties which evaluate a specific part of an image. Each class is highlighted in the segmented image to illustrate the image as a number of separated regions, and the ROI may be one of those regions. Clustering technique is based on multithreshold values which can be set depending on the image histogram. Amira et al

Image segmentation using classification technique.

In the last decade, wavelet transform has been recognized as a powerful tool in a wide range of applications, including image/video processing, numerical analysis, and telecommunication. The advantage of wavelet over existing transforms such as Discrete Fourier Transform (DFT) and Discrete Cosine Transform (DCT) is that wavelet performs a multiresolution analysis of a signal with localization in both time and frequency [

Discrete wavelet transform (DWT) can be implemented as a set of filter banks, comprising a high-pass and low-pass filters. In standard wavelet decomposition, the output from the low-pass filter can then be decomposed further, with the process continuing recursively in this manner. According to [

DWT decomposes the signal into a set of resolution-related views. The wavelet decomposition of an image creates at each scale

Standard and non-standard 2D wavelet transform.

Wavelet Packet (WP) is a wavelet transform where the signal is passed through more filters compared to DWT-based approach. Applying DWT or WP on images generates four coefficients; three of them are the detail coefficients, and the remaining one is the average coefficient. It is worth mentioning that the first level of decomposition is the same for both DWT and WP, as illustrated in Figure

Architecture of Haar filters. (a) DWT, (b) WP.

The differences between DWT and WP can be seen in the detail coefficients where the next decomposition of DWT is applied on the average coefficients from the previous decomposition (Figure

DWT and WP for a phantom slice.

Original image

DWT level1

WP level1

DWT level2

WP level2

DWT level3

WP level3

DWT level4

WP level4

WP full decomposition

Section

3D volume in wavelet domain.

The original volume is transformed into 8 octants (features) in the wavelet domain. Mathematically, 3D-DWT is the process of applying 1D-DWT on each vector in

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Haar filter architecture for 3D-DWT.

Recently, ridgelet transform [

For discrete image data, a projection is computed by summation of all data points that lie within specified unit-width strips; those lines are defined in a finite geometry [

FRAT of a real function on the finite grid

Once the wavelet and radon transforms have been implemented, the ridgelet transform is straightforward. Each output of the radon projection is simply passed through the wavelet transform before it reaches the output multiplier.

As shown in Figure

FRIT block diagram.

Analysing an object with curve singularity implies that ridgelet coefficient will be not sparse and object with curved singularities is still curved or linear after the radon transform where the wavelet transform cannot detect it properly because it is still not a point singularity [

Ridgelet transform for real CT image at different block sizes.

For block-based segmentation using statistical classification, an image is divided into blocks, and a feature vector is formed for each block by grouping statistics of its pixel intensities [

Segmentation in MRFM is achieved by maximizing a posteriori probability of the segmentation depending on a given image data [

Markov chain.

HMMs represent a widespread approach to the modeling of sequences as they attempt to capture the underlying structure of a set symbol strings. The use of HMM for shape recognition has not been widely addressed. Only a few works have been found to have some similarities with the proposed approach. In the first, He and Kundu [

HMM is basically a stochastic finite state automaton, formally defined by the following elements [

When modeling a sequence of observation symbols it is usual to use a so-called “left to right HMM” [

The problem with 2D-HMM is the double dependency of

Pseudo 2D HMM.

Each slice is a two-dimensional matrix which can be classified by an optimum set of states with maximum probability; these states are mapped into classes or segmented objects. The basic assumption of applying HMM on medical images is to use the embedded-HMM by defining a set of Markovian superstates, within each superstate there is a set of simple Markovian states. The superstate is first chosen using a first-order Markov state transition probability based on the previous superstate. A simple Markov chain is then used to generate observations in this superstate. Thus, superstates are related to rows (or any equal size blocks), and simple states are related to columns (or smaller blocks comprised the superstate).

To generate an observation sequence using HMM, an initial state must be chosen according to the initial state distribution; then an observation sequence should be chosen according to the probability distribution in the initial state [

HMM considers observations statistically dependent on neighboring observations through transition probabilities organized in a Markov mesh. Training HMM for images is achieved by dividing the image into nonoverlapping, equally sized blocks, from each of which a feature vector is extracted. Each block and its feature vector evaluate the observation which has its own transition probability matrix. Training HMM produces an estimated state transition probability matrix and estimated emission probability matrix. After building the observation sequence, the model parameters are estimated based on the blocks' statistics. These classes or states were determined using Viterbi algorithm, which depends on

The feature vectors for a testing image are generated to find the set of classes with maximum posteriori according to the trained HMM. The feature vector for each block may be changed at every single state. Once the block state is known, the feature vector will be independent of the other blocks; any two blocks may be more likely to be in the same state if they have close intensities [

The proposed approach has been tested on NEMA IEC body phantom [

(a) NEMA IEC body phantom (DATA SET 1), (b) 2D slice from DATA SET 1, (c) DATA SET 1 after stacking all slices using [

Many techniques can be used for segmentation, and each technique has a different segmentation performance and quality. Listed below are some performance measurement methods that have been used in this paper to test and compare the segmentation techniques.

Dice Similarity Coefficients (DSCs) are a statistical validation metric used to evaluate the performance of both the reproducibility of manual segmentations and the spatial overlap accuracy of automated probabilistic fractional segmentation. The DSC value is a simple and useful summary measure of spatial overlap, which can be applied to studies of reproducibility and accuracy in image segmentation.

The value of a DSC ranges from 0 indicating no spatial overlap between two sets of binary segmentation results to 1 indicating complete overlap [

DSC overlapping.

Euclidean Distance (ED) is the straight line distance between two points. It can be used with DATA SET 1 to compare the measured diameters with the original diameters provided with the phantom description [

The future work of this paper is to segment the medical images automatically in real time and get the results while the patient is waiting. the processing time of the segmentation methods are different, and the processing time may be used as a comparison factor for these methods.

Signal to Noise Ratio (SNR) is also used to differentiate between wavelet and ridgelet output quality. SNR is used in image processing as a physical measure of the sensitivity of an imaging system. Industry standards measure SNR in decibels (dB) of power, and therefore apply the

Parameters in the wavelet transform are points

Wavelet and ridgelet parameters.

Table

Wavelet and ridgelet comparisons depending on SNR and processing time.

Domain | Wavelet | Ridgelet | Satial | ||||

Level 1 | Level 2 | Level 3 | |||||

SNR (dB) | 10.63 | 11.14 | 10.95 | 10.37 | 11.43 | 11.88 | 7.17 |

Time (sec) | 0.23 | 0.24 | 0.50 | 71.5 | 29.91 | 10.01 | 1.18 |

It can be seen from Table

Applying segmentation techniques on 2D slices requires more time compared to the 3D volumes-based approaches time. The time required to look for the best slice that includes the spheres in full diameters is not required in 3D volume segmentation processes. Segmented volume for DATA SET 1 using 3D-thresholding is illustrated in Figure

Error percentage of spheres measurement using different segmentation techniques.

Spheres Diameter (mm) | ||||||||
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MRFM [ | ||||||||

Clustering [ | ||||||||

Iterative Thresholding [ | ||||||||

2D Thresholding | ||||||||

2D-DWT | Haar | Level 1 | ||||||

Level 2 | ||||||||

Level 3 | ||||||||

Daubechies | Level 1 | |||||||

Level 2 | ||||||||

3D Thresholding | ||||||||

3D-DWT |

3D segmentation techniques.

Segmented volume using 3D-thresholding

3D-DWT for DATA SET 1

3D-DWT for DATA SET 2

From Table

Outer diameters have been measured in the case of 3D segmentation, and the inner diameters errors have been calculated based on the thickness of spheres edges. All spheres diameters detected using 3D-thresholding and the errors were over estimated by (0.5–2.5%), they were increasing while the sphere diameter increasing.

Spheres diameters are reduced to the half with each decomposition level of wavelet transform. Three decomposition levels of DWT have been applied on NEMA phantom using two different filters (Haar, Daubechies), and the measured diameters were doubled at each level to produce a fair comparison with the other available techniques. It can be seen that most of the error percentages were decreasing while the spheres diameter increasing, it is worth mentioning that there is no upper bound of the spheres diameters to keep the errors decreasing because the ROI becomes clearer and easier to be detected and measured properly. But tumors in real life are usually very small in the early stage cancer, and the problem is to detect those turnouts as soon as possible.

By applying one decomposition level of 3D-DWT on spatial domain and using the LLL filter output, underestimated percentages have been achieved for the three small spheres (10, 13, and 17 mm) and overestimated percentages for the three big spheres (22, 28, and 37 mm). DWT proved efficient in detecting the big obstacles where the biggest sphere (37 mm) was detected with a very small error percentage (

The two smallest spherical inserts are still underestimated in all techniques except the 3D-thresholding. The large volumetric errors encountered using this acquisition exist as a consequence of the poor slice thickness setting selected for the scan. The 4.25 mm slice thickness causes large fluctuations in transaxial tumor areas to occur between image slices. This problematic characteristic occurs most notably with the smallest spherical inserts, where single voxel reallocation causes a large deviation in percentage error. In Figure

Visual comparison for error percentages.

HMMs have been used for segmentation, which can be applied either in the spatial or multiresolution domain using wavelet or ridgelet transforms. The weakness of HMMs is its long processing time, compared with the other evaluated techniques.

DATA SET 1 has been utilized to perform the experimental study using HMMs and MRA for medical image segmentation, and the achieved results are illustrated in Table

Performance of using HMMs and MRA for medical image segmentation.

diameters (mm) | 10 | 13 | 17 | 22 | 28 | 37 | Processing time (sec) |
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HMM ( | 1.5 | 0.8 | 0.1 | 0.8 | 0.04 | 1 | 2007.3 |

HMM ( | NA* | 11.07 | 7.82 | 2.98 | 1.09 | 0.27 | 1321.1 |

HMM ( | NA* | NA* | NA* | NA* | NA* | 2.41 | 5757.6 |

Segmented image using thresholding technique (a) and HMM (b).

Image Segmentation using HMM. Original (a) and HMM (b)

From Table

It can be seen from Figure

HMMs have been also applied on DATA SET 2 as illustrated in Figure

HMM performance depending on DSC.

Type | joint pixels | No. of pixels | DSC value |
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Spatial | 212521 | 524288 | 0.8107 |

Ridgelet | 158905 | 524288 | 0.6062 |

Image Segmentation using HMM. Original (a), HMM on ridgelet (b), and HMM on spatial (c).

Many techniques have been previously implemented for medical volumes segmentation; some of them were illustrated in this paper and compared with the proposed techniques. Promising results have been achieved using 3D segmentation techniques directly to medical volumes and the statistical models using HMMs; both techniques have the same problem which is the computational time. Many acceleration processing methods have been recently implemented such as FPGAs, Matlab accelerators, Feature Reduction (FR) techniques, GPUs and many more. HMM can be applied with different MRA transforms such as wavelet, ridgelet, and curvelet to achieve promising results. It is worth mentioning that based on the experiments carried out on these specific medical data in this paper, HMMs can be classified as one of the ideal medical volume segmentation techniques compared to the other proposed techniques.

Segmentation is very important for medical image processing, to detect tumors and regions of interest for radiotherapy planning and cancer diagnosis. A novel and sophisticated segmentation system was developed specifically for 3D data segmentation. The developed techniques within the system have been tested on phantom data [

The proposed system was also tested on other data set for real human chest images from a CT scanner and has shown promising results. Ongoing research is focusing on the implementation of other 3D novel feature extraction techniques for medical images based on 3D-ridgelet and 3D-curvelet transforms. In order to speed up the proposed techniques; a graphical processing unit (GPU) will be deployed with more focus on the implementation of higher dimensional HMMs for a more accurate and automatic volume segmentation system.