The experimental study presented in this paper is aimed at the development of an automatic image segmentation system for classifying region of interest (ROI) in medical images which are obtained from different medical scanners such as PET, CT, or MRI. Multiresolution analysis (MRA) using wavelet, ridgelet, and curvelet transforms has been used in the proposed segmentation system. It is particularly a challenging task to classify cancers in human organs in scanners output using shape or gray-level information; organs shape changes throw different slices in medical stack and the gray-level intensity overlap in soft tissues. Curvelet transform is a new extension of wavelet and ridgelet transforms which aims to deal with interesting phenomena occurring along curves. Curvelet transforms has been tested on medical data sets, and results are compared with those obtained from the other transforms. Tests indicate that using curvelet significantly improves the classification of abnormal tissues in the scans and reduce the surrounding noise.
In the last decade, the use of 3D image processing has been increased especially for medical applications; this leads to increase the qualified radiologists’ number who navigate, view, analyse, segment, and interpret medical images. The analysis and visualization of the image stack received from the acquisition devices are difficult to evaluate due to the quantity of clinical data and the amount of noise existing in medical images due to the scanners itself. Computerized analysis and automated information systems can offer help dealing with the large amounts of data, and new image processing techniques may help to denoise those images.
Multiresolution analysis (MRA) [
Image segmentation requires extracting specific features from an image by distinguishing objects from the background. The process involves classifying each pixel of an image into a set of distinct classes, where the number of classes is much smaller. Medical image segmentation aims to separate known anatomical structures from the background such cancer diagnosis, quantification of tissue volumes, radiotherapy treatment planning, and study of anatomical structures.
Segmentation can be manually performed by a human expert who simply examines an image, determines borders between regions, and classifies each region. This is perhaps the most reliable and accurate method of image segmentation, because the human visual system is immensely complex and well suited to the task. But the limitation starts in volumetric images due to the quantity of clinical data.
Curvelet transform is a new extension of wavelet transform which aims to deal with interesting phenomena occurring along curved edges in 2D images [
This paper is focusing on a robust implementation of MRA techniques for segmenting medical volumes using features derived from the wavelet, ridgelet, and curvelet transforms of medical images obtained from a CT scanner. The rest of this paper is organised as follow: Section
The main aim of this research is to facilitate the process of highlighting ROI in medical images, which may be encapsulated within other objects or surrounded by noise that make the segmentation process not easy. Figure
Proposed segmentation system for medical images.
Image segmentation using MRA such as wavelets has been widely used in recent years and provides better accuracy in segmenting different types of images. Many recent developments in MRA have taken place, while wavelets are suitable for dealing with objects with point singularities. Wavelets can only capture limited directional information due to its poor orientation selectivity. By decomposing the image into a series of high-pass and low-pass filter bands, the wavelet transform extracts directional details that capture horizontal, vertical, and diagonal activity. However, these three linear directions are limiting and might not capture enough directional information in noisy images, such as medical CT scans, which do not have strong horizontal, vertical, or diagonal directional elements. Ridgelet improves MRA segmentation; however, they capture structural information of an image based on multiple radial directions in the frequency domain. Line singularities in ridgelet transform provides better edge detection than its wavelet counterpart. One limitation to use ridgelet in image segmentation is that ridgelet is most effective in detecting linear radial structures, which are not dominant in medical images. The curvelet transform is a recent extension of ridgelet transform that overcome ridgelet weaknesses in medical image segmentation. Curvelet is proven to be particularly effective at detecting image activity along curves instead of radial directions which are the most comprising objects of medical images.
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 is that wavelet performs an MRA of a signal with localization in both time and frequency [
Discrete wavelet transform (DWT) can be implemented as a set of high-pass and low-pass filter banks. In standard wavelet decomposition, the output from the low-pass filter can be then 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
For images, 1D-DWT can be readily extended into 2D. In standard 2D wavelet decomposition, the image rows are fully decomposed, with the output being fully decomposed columnwise. In nonstandard wavelet decomposition, all the rows are decomposed by one decomposition level followed by one decomposition level of the columns. Figure
2D DWT filter structure.
Wavelet uses a set of filters to decompose images depending on filter coefficients and the number of those coefficients. The most popular wavelet filter is Haar wavelet filter (HWF) which takes the averages and differences from the low- and high-pass filters, respectively. Figure
2D-DWT. Original image (a), first decomposition level (b), and second decomposition level (c).
In 1998, Donoho introduced the ridgelet transform [
The finite ridgelet transform (FRIT) was computed in two steps: a calculation of discrete radon transform and an application of a wavelet transform. The finite radon transform (FRAT) is computed in two steps: a calculation of 2D Fast Fourier Transform (FFT) for the image and an application of a 1D inverse fast Fourier transform (iFFT) on each of the 32 radial directions of the radon projection. 1D wavelet is applied restricted to radial directions going through the origin for three levels of decompositions.
Applying FRAT on image can be presented as a set of projections of the image taken at different angles to map the image space to projection space. Its computation is important in image processing and computer vision for problems such as pattern recognition and the reconstruction of medical images. For discrete images, 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 [
Depending on [
According to Alzu’bi and Amira in [
FRIT block diagram.
Figure
Ridgelet transform for real CT images at block sizes (3, 7, and 13).
Continuous ridgelet transform is similar to the continuous wavelet transform except that point parameters (
Wavelet and ridgelet parameters.
The segmentation result achieved using ridgelet transformation on medical images was not promising. Medical images comprised from curves which are still not singularity points after applying radon transform. Wavelet transform cannot detect those singularities properly, since it still not singularity points [
Ridgelet transform can be used in other applications, where images contain edges and straight lines. Curvelet transform has been introduced to solve this problem; it deals with higher singularities compared to wavelet and ridgelet transforms.
The curvelet transform has gone through two major revisions. It was first introduced in [
Curvelet aims to deal with interesting phenomena occurring along curved edges in a 2D image. As illustrated in Figure
An approximating comparison between wavelet (a) and curvelet (b).
The newly constructed and improved version of curvelet transform is known as Fast Discrete Curvelet Transform (FDCT). This new technique is simpler, faster and less redundant than the original curvelet transform which based on ridgelets. According to Candes et al. in [ unequally spaced Fast Fourier transforms (USFFT), wrapping function.
Both implementations of FDCT differ mainly by the choice of spatial grid that used to translate curvelets at each scale and angle. Both digital transformations return a table of digital curvelet coefficients indexed by a scale parameter, an orientation parameter, and a spatial location parameter. Wrapping-based transform is based on wrapping a specially selected Fourier samples, and it is easier to implement and understand.
Curvelet transform works in two dimensions with spatial variable
Curvelet tiling of space and frequency. The induced tiling of the frequency plane (a). The spatial Cartesian grid associated with a given scale and orientation (b).
The new implementation of curvelet transform based on Wrapping of Fourier samples takes a 2D image as an input in the form of a Cartesian array
Figure
5-level curvelet digital tiling of an image.
It can be seen from Figure
In order to achieve a higher level of efficiency, curvelet transform is usually implemented in the frequency domain. This means that a 2D FFT is applied to the image. For each scale and orientation, a product of
Wrapping wedge data.
The following are the steps of applying wrapping based FDCT algorithm [
Apply the 2D FFT to an image to obtain Fourier samples
For each scale
Wrap this product around the origin and obtain
Apply IFFT to each
The curvelet transform is a multiscale transform such as wavelet, with frame elements indexed by scale and location parameters. Wavelets are only suitable for objects with point singularities, Ridgelets are only suitable for objects with line singularities, while curvelets have directional parameters and its pyramid contains elements with a very high degree of directional specificity. The elements obey a special scaling law, where the length and the width of frame elements support are linked using
Curvelets are superior to the other transforms as in the following.
Curvelets provide optimally sparse representation of objects which display curve-punctuated smoothness except for discontinuity along a general curve with a bounded curvature. Such representations are nearly as sparse as if the object were not singular and turn out to be far sparser than other transforms decomposition of the object.
Curvelets also have special microlocal features which make them especially adapted to certain reconstruction problems with missing data. For example, in many important medical applications, one wishes to reconstruct an object
As illustrated in (
Figure
Curvelets at increasingly fine scales from 1 to 5. Spatial domain (a, c, e, g, i). Frequency domain (b, d, f, h, j) [
It can be seen from Figure
Clinical slice for the human chest from a CT scanner in spatial (a) and curvelet coefficients (b).
In Figure
Wedge wrapping is done for all the wedges at each scale in the frequency domain to obtain a set of subbands or wedges at each curvelet decomposition level, and these subbands are the collection of discrete curvelet coefficients.
The aim is to identify the most effective texture descriptor for medical images to capture edge information more accurately. The discrete curvelet transform can be calculated to various resolutions or scales and angles; the maximum number of resolution depends on the original image size and the angles. Number of angles at the second coarsest level must be at least eight and a multiple of four; that is,
Reconstruction of tomographic data. Wavelet domain (a), and curvelet domain (b).
The end users of the proposed system are the radiologists and specialists who analyse medical images for cancer diagnosis. After several meetings with those people in the radiology departments in some hospitals, the main goal that they are working is to detect the accurate cancer size in medical images with the least error. This process may be affected by the noise surrounding ROI, which make the process of measuring the exact dimensions of the lesion so hard.
Different datasets have been carried out with the proposed system to validate it for clinical applications. The first one is NEMA IEC body phantom which consists of an elliptical water filled cavity with six spherical inserts suspended by plastic rods of inner diameters: 10, 13, 17, 22, 28, and 37 mm [
Wavelet and ridgelet comparisons depending on SNR and processing time.
Domain | Wavelet | Ridgelet | Spatial | ||||
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
MRA transforms have been used with thresholding technique to segment the experimental data. Thresholding technique has been applied as a preprocessing step on the original images at threshold value (
Figure
Curvelet transform for segmentation. (a) NEMA IEC body phantom, (b) segmented phantom slice, (c) original real chest slice, and (d) segmented real chest slice.
Segmentation using conventional hard thresholding and curvelet-based segmentation. (a) Denoised spatial domain. (b) First level in wavelet domain. (c) Ridgelet domain. (d) Curvelet domain.
Table
The error percentages of spheres diameters measurements for NEMA IEC body phantom.
Spheres (mm) | Error % for measured diameters | |||||||
10 | 13 | 17 | 22 | 28 | 37 | |||
K-means [ | −13.6 | −11.5 | −5.77 | −5.51 | −5.1 | −5.01 | ||
MRFM [ | −7.41 | −8.69 | 4.28 | 4.06 | 3.9 | 3.89 | ||
Clustering [ | 16.0 | 9.0 | 1.1 | |||||
Iterative Thresholding [ | 3.0 | |||||||
Wavelet | ||||||||
Haar | ||||||||
Level 1 | −2.9 | −2.46 | 1.35 | 0.82 | 0.29 | 0.05 | ||
Level 2 | −1.95 | |||||||
Level 3 | — | — | −3.24 | |||||
Daubechies | ||||||||
Level 1 | 2.0 | 1.81 | ||||||
Level 2 | −0.11 | |||||||
Ridgelet | −10.93 | −6.67 | 3.88 | −1.30 | −0.76 | −1.95 | ||
Curvelet | 2.65 | 1.62 | 1.07 | −0.82 | −0.33 | −0.09 |
From Table
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 [
The two smallest spherical inserts are still underestimated in most of the techniques and got the largest error percentages. 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 tumour 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 in Table
It can be also seen from Table
Curvelet transform overcomes the weakness of wavelet for segmenting sharp curves and detect the small spheres accurately with error percentages (0.82%–2.65%). For the big spheres, errors achieved using wavelet transform are still better than those achieved using curvelet transform due to the sharpness of that spheres. But still very good results using curvelet transform and acceptable for clinical applications.
PSNR and MSE have been also used to evaluate the quality of the proposed techniques. The original image has been contaminated with Gaussian white noise at
Comparison of curvelet, ridgelet, and wavelet denoising in terms of PSNR and MSE.
Image name | Curvelet denoising | Ridgelet denoising | Wavelet denoising | |||
MSE | PSNR (dB) | MSE | PSNR (dB) | MSE | PSNR (dB) | |
NEMA | 41.67 | 31.93 | 108.78 | 26.14 | 101.12 | 28.08 |
Chest | 58.8 | 30.44 | 152.45 | 23.55 | 147.63 | 26.44 |
From Table
MRA for image denoising. (a, d) Noisy images. (b, e) Wavelet. (c, f) Curvelet.
According to a study done by Dettori and Semler [
Curvelet-based descriptors had an even higher performance in comparison to both the wavelet and ridgelet, with accuracy rates higher, respectively. The accuracy rate using curvelet transform is better; this is expected, since the curvelet transform is able to capture multidirectional features in wedges, as opposed to lines or points as in the ridgelet or wavelet transform. The multidirectional features in curvelets are very effective in extracting the important features from medical images and then segmented accurately.
As illustrated in the previous tables and figures, it can be seen that more efficient and smooth image reconstruction is achieved using curvelet transform. In terms of optimal reconstruction of the objects with edges and curves, curvelet-based techniques outperform the traditional wavelet and ridgelet transforms.
The algorithm presented in this chapter is able to classify normal tissues in CT scans with high accuracy rates. These hypotheses will be further tested and validated on different predefined clinical data sets in chapter 8 of this thesis.
Segmentation using curvelet transform has been chosen for experimenting the PET scanner sensitivity variables, curvelet was applied in parallel with multithresholding and classification techniques to classify the spheres in a separate class from the other comprising objects at least noise included. The experiment was evaluated based on the ratio between the spheres area to the other area of the scanned slice. The actual spheres area can be calculated according to (
Spheres to background ratio (SBR) for different variable samples.
2D/3D | Time/bed section | Iteration | SUB | SBR (%) |
---|---|---|---|---|
2D | 2 min | 1 | 30 | 0.46 |
2D | 2 min | 5 | 30 | 0.31 |
2D | 2 min | 10 | 30 | 0.24 |
2D | 2 min | 30 | 30 | 0.22 |
2D | 3 min | 1 | 30 | 0.56 |
2D | 3 min | 5 | 30 | 0.59 |
2D | 3 min | 10 | 30 | 0.55 |
2D | 3 min | 20 | 30 | 0.53 |
2D | 4 min | 3 | 30 | 0.55 |
2D | 4 min | 15 | 30 | 0.42 |
2D | 4 min | 20 | 30 | 0.36 |
2D | 4 min | 30 | 30 | 0.31 |
3D | 2 min | 1 | 32 | 1.1 |
3D | 2 min | 3 | 32 | 0.76 |
3D | 2 min | 7 | 32 | 0.71 |
3D | 2 min | 10 | 32 | 0.69 |
3D | 3 min | 1 | 32 | 1.02 |
3D | 3 min | 3 | 32 | 0.77 |
3D | 3 min | 10 | 32 | 0.71 |
3D | 3 min | 15 | 32 | 0.68 |
3D | 4 min | 3 | 32 | 0.74 |
3D | 4 min | 10 | 32 | 0.68 |
3D | 4 min | 30 | 32 | 0.64 |
Scanner variables effects on the segmented image.
It can be seen from Figure
Segmented results achieved at IT value (10), where the best results detected.
A predefined clinical dataset comprised of 217 slices, with slice thickness of 3.0 mm has been tested on the proposed system. Based on the provided report, the patient is affected by multiple bilateral renal cortical cysts; the largest one is seen in the lower pole of the right kidney, measuring about
AMIDE snapshot locating the kidney cancer.
ROI highlighted in the original image (kidney cancer).
MRA have been applied on the medical image to segment it and detect ROI. Figure
MRA for real clinical data segmentation.
The performance of the proposed techniques for segmenting the illustrated slice in Figure
Segmentation techniques’ performance based on patient data (kidney cancer data).
Segmentation technique | Cancer area accuracy (%) | MSE | PSNR (dB) | Data loss | |
DWT | |||||
Haar | 91.0 | 102.7 | 35.2 | Normal | |
Daubechies | 89.5 | 104.5 | 34.3 | Normal | |
Wavelet Packet | 83.2 | 111.2 | 30.9 | Normal | |
Ridgelet | — | 109.9 | 30.3 | High | |
Curvelet | 96.2 | 88.2 | 29.5 | Normal |
The clinical datasets have been segmented also using 3D segmentation techniques, and the lesions were detected accurately. Curvelet transform has been used before 3D segmentation to achieve a denoised CT output and ensure smoother edges. Patient data which includes lesions in liver, kidney and lung has been segmented and visualized in Figures
Segmenting patient volume data affected by the kidney cancer.
Segmenting patient volume data affected by the lung cancer.
Segmenting patient volume data affected by the liver cancer (located by red arrows).
Due to the changing shapes of organs in medical images, segmentation process using multiresolution analysis combined with thresholding as pre- and postprocessing step allows accurate detection of ROIs. Multiresolution analysis such as wavelet transform is extensively used in medical image segmentation and provides better accuracy in results. Curvelet and ridgelet transforms are new extension of the wavelet transform that aims to deal with interesting phenomena occurring along higher dimensional singularities. Though wavelets are well suited to point singularities, they have limitations with orientation selectivity hence do not represent changing geometric features along edges effectively. Curvelet transform exhibits good reconstruction of the edge data by incorporating a directional component to the traditional wavelet transform. Experimental study in this report has shown that curvelet-based segmentation of the medical images not only provide good-quality reconstruction of detected ROI, promising results are also achieved in terms of accurately detecting ROI and denoising process. Curvelet transform is a new tool and utilization of this technique; it is far from sufficient in the medical image processing area. The future work related to this is the implementation of 3D MRA transform which can be applied directly on medical volumes to detect obstacle and objects of interest.