Recent multiscale AMFM methods in emerging applications in medical imaging
 Victor Murray^{1}Email author,
 Marios S. Pattichis^{1},
 Eduardo Simon Barriga^{1, 2} and
 Peter Soliz^{2}
DOI: 10.1186/16876180201223
© Murray et al; licensee Springer. 2012
Received: 24 March 2011
Accepted: 8 February 2012
Published: 8 February 2012
Abstract
Amplitudemodulation frequencymodulation (AMFM) decompositions represent images using spatiallyvarying sinusoidal waves and their spatiallyvarying amplitudes. AMFM decompositions use different scales and bandpass filters to extract the wide range of instantaneous frequencies and instantaneous amplitude components that may be present in an image. In the past few years, as the understanding of its theory advanced, AMFM decompositions have been applied in a series of medical imaging problems ranging from ultrasound to retinal image analysis, yielding excellent results. This article summarizes the theory of AMFM decompositions and related medical imaging applications.
Keywords
multidimensional AMFM methods digital image processing medical imaging1. Introduction
In the field of computer aided detection and diagnostics (CAD), recent advances in image processing techniques have brought a wide array of applications into the field. Many existing CAD methods rely on fixed basis functions based on wavelet decompositions [1] and Gabor filters [2]. AmplitudeModulation FrequencyModulation (AMFM) methods [3–6] represent an emerging technique that shows great promise in this area.
Multidimensional AMFM models and methods provide us with powerful, image and video decompositions that can effectively describe nonstationary content. They represent an extension to standard Fourier analysis, allowing both the amplitude and the phase functions to vary spatially over the support of the image, following changes in local texture and brightness.
where a_{ n }(x, y) denote slowlyvarying instantaneous amplitude (IA) functions, φ_{ n }(x, y) denote the instantaneous phase (IP) components, and n = 1, 2,..., M indexes the different AMFM harmonics. In (1), the n th AMFM harmonic is represented by a_{ n }(x, y) cos φ_{ n }(x, y).
With each phase function, the instantaneous frequency (IF) vector field is defined by $\nabla {\phi}_{n}\left(x,y\right)$. Here, the AMFM demodulation problem is defined as one of determining the IA, IP, and IF functions for any given input image.
AMFM decompositions provide physically meaningful texture measurements. Significant texture variations are captured in the frequency components. For single component cases, IF vectors are orthogonal to equiintensity lines of an image, while the IF magnitude provides a measure of local frequency content. In (1), by using AMFM components from different scales, we can produce IF vectors from different scales, at a pixellevel resolution [4, 5].
Since AMFM texture features are provided at a pixellevel resolution, AMFM models can be used to segment texture images that are difficult to model with the standard brightnessbased methods [7]. On the other hand, using just histograms of the IF and IA, we can design effective contentbased image retrieval systems using very short image feature vectors [8, 9].
In summary, the advantages of AMFM methods include [10]: (i) they provide a large number of physically meaningful texture features, over multiple scales, at a pixellevel resolution, (ii) the image can be reconstructed from the AMFM decompositions, (iii) based on the target application, different AMFM decompositions using different frequency coverage can be designed, and (iv) very robust methods for AMFM demodulation have been recently developed (see some recent examples in [4]).
where each AMFM function has been extended to be a function of both space and time. The original phasebased modeling approach was provided in [11] and was recently extended and improved in [12, 13].
AMFM decompositions can also be used to reconstruct the input images, allowing us to evaluate their effectiveness on different parts of the image. For continuousspace image decompositions, AMFM reconstruction examples can be found in [14], while [4, 5] give several recent, robust multiscale examples for both images and videos. AMFM transform examples were shown in [15], while multidimensional orthogonal FM transforms were demonstrated in [16].
An early example of the use of frequencydomain filtering to target a particular application can be found in the fingerprint examples in [17]. More recently, [18] provided a treegrowth application, where interring spacing was used to design filterbanks that cover a specific part of the spectrum, so as to recover tree ring and tree growth structure from very noisy image inputs. For general images, Gabor filterbank approaches were investigated in [3]. Similarly, for general images and videos, dyadic, multiscale decompositions were introduced in [4].
A summary of AMFM methods is provided in Section 2. Results are presented for several medical imaging applications in Section 3. Finally, conclusions and future work are presented in Section 4.
2. Methods
2.1. Multidimensional AMFM demodulation methods
Recent interest in the development of multidimensional AMFM methods can be traced to early work on speech signal models by Jim Kaiser. In early work, Dr. Kaiser developed on algorithms for estimating the energy of ID signals in [19–21]. This led to the development of the ID and 2D energy separation algorithm (ESA) as described in [22–24]. Maragos et al. continued with the ID AMFM work previously mentioned for ID application in [22, 23, 25, 26]. Early work on multidimensional energy separation methods appeared in [27]. AMFM demodulation based on Gabor wavelets appeared in [28, 29]. Early research on the use of multidimensional energy operators continued in [24, 30]. In what follows, we begin with an introduction to multidimensional energy operators.
where ${\widehat{\phi}}_{y}$, is estimated by replacing the xderivative by the yderivative in (4). To eliminate sign ambiguities, the TeagerKaiser operator can select the candidate IF for which the image gives the largest projection (e.g., see [31]). Recently, Kokkinos et al. showed a related accurate demodulation method using energy operators in [32] by computing all necessary derivatives by convolving with derivatives of Gabor filters, as opposed to using finite differences. The IA estimates are corrected by dividing by the magnitude response of the Gabor filter at the estimated IF (see [32] for details).
Analytic image methods for AMFM demodulation are based on providing a Hilbertbased extension of the ID Hilbertbased demodulation approach. Here, the basic idea is to simply apply the ID Hilbert operator along the rows (or the columns). The fundamental advantage of this approach is that it preserves the 2D phase and magnitude spectra of the 2D input image. In fact, implementation involves taking the 2D FFT of the input image, removing spectral frequency with a negative rowfrequency component, multiplying the result by 2, and taking the inverse 2D FFT. Given the conjugate symmetry of 2D images, the removal of two frequency quadrants does not result in the loss of any spectral information. Furthermore, it can be shown that for singlecomponent AMFM signals, this can lead to exact demodulation. In practice though, we replace derivatives by finite differences. We will further elaborate on this method in Section 2.2. For early work on this approach we refer to Havlicek's dissertation [3]. Havlicek et al. [3, 33–41] presented the first results for TVdimensional signals using the quasieigenfunction approximation (QEA) method (see Section 2.2).
Both ESA and Hilbertbased methods share the use of a filterbank prior to AMFM demodulation. The basic idea is to use a filterbank to be able to separate out among different AMFM components. AMFM demodulation is then applied at the output of each channel filter. Here, it is important to note that in the event that two AMFM components fall within the same channel filter, the filterbank approach will not allow us to separate them. Here, new algebraic approaches should be considered.
The filterbank generates AMFM demodulation outputs for each channel. Both ESA and Hilbertbased methods select estimates from a dominant component. For ESA, the dominant component is selected based on an energy criterion. In QEA, the dominant component is often selected based on the maximum IA estimate. Here, please note that a single channel is selected over the entire filterbank. In a multiscale approach, instead of selecting dominant components over the entire filterbank, we select the dominant channel from a collection of channels. The basic idea is to define scales based on the frequency magnitude. The most popular approach is to define low, medium, and high frequency scales (see examples in [4]).
Another robust approach for computing AMFM estimates based on a quasilocal method was developed in [42–44] for 1D signals. This methodology was extended to digital images in [5, 45]. Furthermore, in [5], we have a comparison of ESA, Hilbertbased, and the quasilocal methods for a variety of 2D AMFM signals. From the comparisons, we note that the choice of the filterbank can have a dramatic effect on the estimation. Flat passbands tend to help with the IA estimation. On the other hand, Gaborbased filterbanks are easy to design and implement and they can perform very well on IF estimation.
Thus, the quadraturephase transform does not alter the magnitude of the AMFM signal. On the other hand, the same cannot be said about the phase. The phase information is not longer preserved. By examining (7), we can see that this is especially problematic for high frequencies (H).
The phase and magnitude of the monogenic signal f_{ M }are then taken as the phase and magnitude of the AMFM signal. This is also extended to multiple scales in the multiresolution framework of [51], and into scalespace in [49]. Other related work on image demodulation based on the Riesz transform extension has been reported by Mellor, Noble, Hahn, Felsberg, Sommer and collaborators in [48, 52–57]. In (8), it is important to note that while the input signal is 2D, the generated monogenic signal is actually 3D. This was done to extend the ID analytic properties to 2D. On the other hand, it is also clear that these 2D convolutions will also alter the phase of the 2D input AMFM signal. In fact, as can be seen in the fingerprint example of Figure eleven of [51], the estimated amplitudes contains the ridges. In contrast, in the ESA fingerprint examples of [6], the ridges are modeled as a FrequencyModulation process. This is a fundamental difference in the different approaches considered here.
Similar to AMFM methods, we mention the work by Knutsson et al. for representing local structures on phase using tensors [58–60]. Furthermore, the complex Wavelet transform provides an extension to the discrete wavelet transform that is related to the 2D Hilbertspace extension [61–65].
2.2. Multiscale AMFM methods
In this section, we provide more details on the use of multiplescales in AMFM demodulation. Many of the concepts introduced in this section are shared by the AMFM demodulation methods described in Section 2.1.
where n = 1, 2, ..., M denote different scales [4, 5]. In (9), a continuous image I(x, y) is a function of a vector of spatial coordinates (x, y). A collection of M different scales are used to model essential signal modulation structure. The amplitude functions a_{ n }(·) are always assumed to be positive.
The IF vector ∇φ_{ n }(·) can vary continuously over the spatial domain of the input signal.
The effect of either operation is to generate a complexvalued signal estimates of the form: a(x, y) exp (jφ(x, y)), where the IA and phase functions will hopefully approximate the input AMFM components. Then, a collection of bandpass filters is used to isolate the individual AMFM components [3].
The basic assumption here is that different AMFM components will be picked up by different bandpass filters at the same image region. In other words, given any local image region the assumption is that the corresponding AMFM components will be separated by the use of different filters in the interbank.
In discrete terms (see Figure 1), given the digital input image I(k_{1}, k_{2}) (where k_{1} and k_{2} are the discrete versions of x and y, respectively), the application of an analytic extension generates an "analytic signal" of the form: I_{ AS }(k_{1}, k_{2}). This 2D extension is processed through a collection of bandpass filters (to be described in the Section 2.3) within the desired scale. Each processing block will produce the IA, the IP, and the IF in both x and y directions. At the output of each block, the IA and the IP are estimated by simply taking the magnitude and the phase of the output.
In dominant component analysis (DCA), for each pixel approach, the best AMFM demodulation estimates are selected from the bandpass filter that produces the largest IA estimate. For energybased approaches, the dominant channel is selected based on the maximum energy estimate. Hence, the algorithm adaptively selects the estimates from the bandpass filter with the maximum response. This approach does not assume spatial continuity, and allows the model to quickly adapt to singularities in the input signal (both high and low frequency changes).
where ${\u012a}_{AS}\left({k}_{1},{k}_{2}\right)={\xce}_{AS}\left({k}_{1},{k}_{2}\right)/\left{\xce}_{AS}\left({k}_{1},{k}_{2}\right)\right$, and n_{1} represents a variable displacement that varies from 1 to 4. Variable spacing, local linear phase (VSLLP) produces the most accurate of the four estimates by considering the condition number of the arccos(·) function [4, 5]. Similarly, the approach is repeated for the second direction. It turns out that VSLLP reduces to the earlier method of QEA for the special case when n_{1} = n_{2} = 1 (see [3] for QEA).
2.3. Filterbank design
For computing the AMFM estimates, the AMFM components need to be isolated from (9) using a multiscale filterbank. Here, the basic idea is to isolate different AMFM components over different frequencies (see [66] for details). Figure 2 (a) depicts the frequency support for a dyadic filterbank decomposition.
In Figure 2, the low pass filter (LPF, with label number 1) has frequency support in [π/16, π/16] radians for both the x and y directions. The filters in the highest frequencies (filters from 2 to 7 in Figure 2), have a bandwidth of π/2 for both x and y directions. The bandwidth is decreased by a factor of 0.5 for each added scale. In Figure 2 (b), a closeup that shows the low frequency filters is provided.
The scales are provided using a collection of bandpass filters as: (i) LPF, (ii) very low frequencies (VL), (iii) low frequencies (L), (iv) medium frequencies (M) and (v) H as given in [4], When the structures are well defined in sizes, the measurements can be related with specific instantaneous wavelengths described in number of pixels [67, 68].
CoS used for computing the dominant AMFMfeature parameters
CoS*  Scales used  CoS*  Scales used 

1  VL, L, M, H  7  LPF, VL 
2  LPF  8  VL, L 
3  VL  9  L, M 
4  L  10  M,H 
5  M  11  H 
6  LPF, VL, L, M, H 
Relationship among ILO standard grades for rounded opacities and the size in mm, size in pixels and range in frequency
Type of rounded opacities  Range in mm  Range in pixels  Range in lowest frequency content 

P  Up to 1.5  Up to 18  [π/9, π] 
q  1.53  1836  [π/18, π/9] 
r  310  36120  [π/36, π/18] 
2.4. Postprocessing methods
2.4.1. Histogram features
AMFM features can be summarized using appropriately chosen histograms. Here, we provide a summary of how this can be accomplished.
For each of the 11 CoS (see Table 1), a 96bin feature vector that contains the AMFM histograms is created. Each AMFM histogram has the information of (32bin each): (i) the IA, (ii) the IF magnitude, and (iii) the IF angle. Thus, each image produces 11 different feature vectors, each one corresponding to one of the 11 different CoS.
Since the AMFM estimates of neighboring pixels could be affected by noisy estimates, a 9 × 9 median filter is often applied to the output of the IA and IF estimates (see [4, 5, 14]). We refer to [70] for methods that can be used to adaptively set the median filter window size.
Due to the ambiguity of the IF vectors (coming from cos φ(k_{1}, k_{2}) = cos(φ(k_{1}, k_{2}))), the IF estimates are mapped to two frequency quadrants:

Instantaneous frequencies $\frac{\partial {\phi}_{n}}{\partial x}\left(x,y\right)\ge 0$ and $\frac{\partial {\phi}_{n}}{\partial y}\left(x,y\right)\ge 0$ are kept as they are.

Instantaneous frequencies $\frac{\partial {\phi}_{n}}{\partial x}\left(x,y\right)\ge 0$ and $\frac{\partial {\phi}_{n}}{\partial y}\left(x,y\right)<0$ are kept as they are.

Instantaneous frequencies $\frac{\partial {\phi}_{n}}{{\partial}_{x}}\left(x,y\right)<0$ and $\frac{\partial {\phi}_{n}}{\partial y}\left(x,y\right)<0$ are mapped to $\left\frac{\partial {\phi}_{n}}{\partial x}\left(x,y\right)\right$ and $\left\frac{\partial {\phi}_{n}}{\partial y}\left(x,y\right)\right$.

Instantaneous frequencies $\frac{\partial {\phi}_{n}}{{\partial}_{x}}\left(x,y\right)<0$ and $\frac{\partial {\phi}_{n}}{\partial y}\left(x,y\right)\ge 0$ are mapped to $\left\frac{\partial {\phi}_{n}}{\partial x}\left(x,y\right)\right$ and $\left\frac{\partial {\phi}_{n}}{\partial y}\left(x,y\right)\right$.
Then, the IF histograms are computed.
For the IF angle, given by arctan $\left(\frac{\partial {\phi}_{n}}{\partial y}\left(x,y\right)/\frac{\partial {\phi}_{n}}{\partial x}\left(x,y\right)\right)$, the histogram is centered around the maximum value using:
[h] ← histogram [IF angle using l bins] {Where h is a column vector.}
H ← [hhh]. {Triplicate version of h.}
i ← Location of the maximum value of h.
h ←H_{l+il/2+l:l+i+l/2}.
As last step, all the computed histograms (IA, IF magnitude, and IF angle) are normalized such that the cumulative sum of each one is equal to 1. Thus, the bins will now correspond to the probability density function (PDF) estimates.
2.5. Partial least squares classification of AMFM features
The histograms of AMFM features can be used in classification applications. Here, we introduce a promising classifier based on Partial least squares.
where y is a n × 1 vector of the classification variables, X is a n × p matrix of the extracted AMFM features, β is a p × 1 vector of regression weights, and ε is a n × 1 vector of residuals. The least squares solution to estimating β is given by the normal equations β = (X^{ T }X)^{l} (X^{ T }y).
In most of medical imaging applications, there are much more features than images (p <n), and AMFM features in X are highly correlated. Thus, X^{ T }X canbe singular or nearly singular and a unique solution to the normal equations will not exist. PLS reduces X to a lower dimensional subspace (k ≪ p). The first step is to factor X as X = TL, where T is an orthogonal n × k matrix of Tscores and L is a k × p matrix of factor loadings. The Tscores matrix are used to find a threshold for classification as outlined in [72],
2.6. Morphological segmentation
AMFM features can also be used for image segmentation. A simple Bayesian classification scheme based on the IA and IF magnitude was demonstrated in [7].
where I_{ s }is the binary segmented image, B is the structural element; nB is the result of n dilations of B by itself; ○ the standard open operation and • the standard close operation.
The value of n needs to be chosen so that the smaller, noisy structures are removed, while the larger structures are preserved. Once the order of the morphological filter is calculated, the segmented image is denoised using (13).
3. Applications in medical imaging
Select list of AMFM applications in Biomedical Imaging
Author  Filterbank  AMFM Demodulation Method  Medical Application 

Fleet and Jepson 1990 [11]  3D Gabor filterbank  See section 3.1.  Motivated applications of motion estimation based on phasebased methods. See HARP method in [74]. 
Pattichis et al. 2000 [7]  Gabor filterbank  QEA  Electron microscopy image segmentation 
Maragos et al. 2002 [78]  1D Gabor filterbank  ESA  Doppler ultrasound spectroscopy resolution 
Gabor filterbank  QEA and continuousspace demodulation  Demonstrated AMFM reconstructions of breast cancer images  
Boudraa et al. 2006 [77]  Cross Ψ_{ B }energy operator  Nuclear cardiac sequences for one normal and four abnormal cases  
Alexandratou et al. 2006 [79]  Gabor filterbank  Vectorvalued ESA for color images  Ploidy image analysis (cancer). 
Murray et al. 2007 [13]  Dyadic 3D filterbank (optimal design)  QEA + new AM and FM motion estimation  Motion Estimation for Atherosclerotic Plaque videos compared against other Phasedbased method 
Murray et al. 2008 [8], Agurto et al. 2008 [85] and Barriga et al. [86]  Dyadic 2D filterbank  New VSLLP method  Retinal image analysis. 
Gabor  QEA  Optical coherence tomography.  
Dyadic 2D filterbank  QEA implementation using SIMD  Cardiac applications including Wireless Transmission.  
Gill et al. 2005 [117]  1D monocomponent AMFM  Detection and identification of heart sounds.  
Ramachandran et al. 2001 [102, 109], Pattichis et al. 2002 [103] and Murray etal. 2009 [67, 68]  Polynomial 2D filterbank [102, 103, 109] and Dyadic 2D filterbank (optimal design) [67, 68]  Hilbertbased AMFM  Analysis of pneumoconiosis XRay images. 
Nguyen et al. 2008 [91]  1D filters and Kalman filters  1D Hilbert based AMFM  Analysis of Electroencephalography. 
Christodoulou et al. 2009 [80, 81] and Loizou et al. 2009 [82]  Dyadic 2D filterbank  New VSLLP method  Segmentation and classification in the carotid artery. 
Belaid et al. [97]  Quadrature filters [49]  Monogenic Signal.  Segmentation of ultrasound images. 
An interesting application of AMFM models in motion estimation was presented by Fleet and Jepson [11]. In [11], Fleet and Jepson use a 3D Gabor interbank to estimate optical flow motion at pixellevel resolution. Their approach motivated the later application of a harmonic phase (HARP) method in [74].
In one of the earlier applications in electron microcopy, a simple Bayesian method using the IA and the IF was used, in conjunction with morphological filtering to provide segmentations of different abnormalities over 26 images [7]. Elshinawy et al. [75, 76] demonstrated the reconstruction of breast cancer images using AMFM components.
Boudraa et al. [77] introduced a new crossenergy operator and used the operator to demonstrate the functional segmentation of dynamic nuclear images. Maragos et al. provide an important application for ultrasound spectroscopy in [78], where AMFM models are used for improving Doppler ultrasound resolution. Vectorvalued based AMFM demodulation is given in [79] by Alexandratou et al. Multiscale AMFM methods were applied to chest radiographs [67, 68], ultrasound images of the carotid artery [80–83], image retrieval in ophthalmology by Acton et al. [84], retinal image classification [8, 85, 86], and electron microscopy [7].
We also have some related 1D medical signal applications by different research groups. Relevant 1D AMFM methods appear in [87–90]. Medical applications include the classification of surface electromyographic signals in [80], and the analysis of brain rhythms in electroencephalograms [91].
More general (nonmedical) AMFM applications in tracking include the work reported by Prakash et al. [92, 93] and Mould et al. [94]. Recent AMFM texture analysis research is also reported by Kokkinos et al. [95] and Tay et al. [96]. Recently, Belaid et al. [97] presented an ultrasound image segmentation method based on the monogenic signal and quadrature filters [49].
In the rest of this section, we provide recent examples from the application of multiscale AMFM decompositions to biomedical imaging. While the applications are focused on the particular models described in Section 2.2, it is important to note that new applications are expected, especially from methods based on multidimensional energy operators and methods based on the monogenic signal.
3.1. Optical flow motion estimation
One of the earliest applications of AMFM methods comes from the application of phasebased method in estimating opticalflow motion. Here, we use the term "opticalflow motion" to differentiate it from actual object motion. We begin with a formulation of optical flow motion and proceed to describe the phasebased approach.
Let the image intensity in a digital video sequence be denoted by I(x, y, t). After a sufficiently small time interval Δt, the intensity at (x, y) will move to a point (x + Δx, y + Δy). Here, we are assuming that the image intensity is preserved: I(x + Δx, y + Δy, t + Δt) = I(x, y, t).
In (14), at every pixel, we have a single equation in two unknowns. This forces us to add additional constraints. For example, a continuity constraint requires that the solution keeps the spatial integral of ${u}_{x}^{2}+{u}_{y}^{2}+{v}_{x}^{2}+{v}_{y}^{2}$ small over the solution small. With this additional constraint we end up with two equations for two unknowns per pixel.
where (k_{ i }, w_{ i }) is the peak tuning frequency of the i th filter, σ_{ k }is the standard deviation of the filter's amplitude spectrum, and τ is a threshold used to reject unreliable estimates of instantaneous frequencies. Similarly, for the amplitude, they require that the local signal amplitude must be as large as the average local amplitude, and at least 5% of the largest response amplitude across all the filters at that frame. When either one of these two conditions is not met, the method does not provide velocity estimates.
where the local velocity estimate at the central pixel is given by (α_{0}, β_{0}).
This study represents an important early application of an AMFM model to motion estimation. It provided the motivation to the recent work in estimating cardiac motion from MRI (see HARP method in [74]). We expect to see the emergence of new, multiscale AMFM methods that would be applied to motion estimation from medical video.
3.2. Retinal image analysis
Diabetic retinopathy (DR) and agerelated macular degeneration (AMD) are two retinal diseases that present particular characteristics (lesions) on retinal photographs which can be used in early detection and/or classification of the disease. DR and AMD affect individuals in their most productive years of life. Early detection that leads to prevention of vision loss, alone, will lead to significant decrease in risk of early vision loss.
According to the National Eye Institute, DR is one of the leading causes of blindness among workingage Americans, while macular degeneration is a leading cause of blindness among older Americans [98]. It has been shown that regular comprehensive eye exams and timely treatment can lead to improved outcomes and reduced loss of vision. However, to screen the tens of millions at risk for DR would tax the healthcare system beyond capacity. Results of an automatic DR screening system based on AMFM exhibit strong promise in addressing this problem.
AMD is the most common cause of visual loss in the United States and is a growing public health problem. One third of Americans will develop AMD in their lifetimes. To detect AMD, retinal images are graded using the agerelated eye disease study (AREDS) protocol for human grading. AMFM has been used to develop an automated system for characterizing pathological features on these images.
3.2.1. Diabetic retinopathy
Images correctly classified per risk
Risk  Number  Percentage (%) 

3  68  97 
2  32  82 
1  8  89 
0  38  54 
After all the images were processed with AMFM, they were divided in regions of 100 × 100 pixels avoiding the optic disc. Feature vectors were calculated using the moments in each region: mean, standard deviation, skewness, and kurtosis. Finally, the information per image is the input for the PLS algorithm were the algorithm is trained to classify normal images vs abnormal images.
The results obtained with this approach show an area under the ROC curve of 0.84 with best sensitivity/specificity of 92%/54%. Table 4 (last column) shows the number of images correctly classified per risk level [9]. On this table we can see a large percentage of the highrisk patients are being classified correctly.
3.2.2. Agerelated macular degeneration
Mahalanobis distance between retinal features: Retinal Background (RB), Hard Drusen (DRH), Soft Drusen (DRS), and Vessels
RB  DRH  DRS  Vessels  

RB    3.37  5.56  5.34 
DRH      2.82  4.42 
DRS        4.50 
Vessels         
The numbers in Table 5 represent the standard deviations separating the histograms of the retinal structures. The entries under hard drusen (DRH) and soft drusen (DRS) show that they are significantly differentiated from other structures in the retina. A distance of 3 standard deviations represents a classification accuracy of more than 90%. The most interesting entry is the Mahalanobis distance between the two drusen types (2.8 standard deviations). Though still considered a high classification rate (85%), this demonstrates the challenge not only to the algorithm, but for the grader in unequivocally assigning drusen to one class or another.
3.3. Pneumoconiosis in chest radiographs
The chest radiograph is an essential tool used in the screening, surveillance, and diagnosis of dustrelated respiratory illness resulting from silica and coal dust, asbestos, and a variety of other dusts that can lead to disease. The standardized method used by the international labor organization (ILO, [69]) for interpreting the chest radiograph for inorganic dustinduced diseases or pneumoconioses has been widely utilized for the past five decades.
Two limitations of the current ILO system are the intra and interinterpreter variability and the time consuming process of interpreting large numbers of radiographs taken for screening and surveillance programs. Murray et al. [67, 68] have developed a technique based on AMFM that detects the level of pneumoconioses based on the nodule formation on the lungs.
Currently, the US remains 6th in the world for pneumoconiosis and interstitial lung disease (ILD) or pulmonary interstitial fibrosis as large numbers of workers continue to be exposed to dust in their work environment. Coal workers' pneumoconiosis (CWP) is identified by a specific pattern of XRay abnormalities and a history of exposure to coal dust. The chest radiograph is the single most useful tool for clinically evaluating both occupationally related and nonoccupational chronic lung diseases. The chest radiograph is an essential tool used in the screening, surveillance, and diagnosis of dustrelated respiratory illness resulting from silica and coal dust, asbestos, and a variety of other dusts that can lead to disease.
An AMFM method for grading chest radiographs according to the ILO standards is presented in [67, 68] by Murray et al. Related work, by different research groups, can be found in [102–108]. First, a logarithmic transformation to the images is applied to improve the contrast of the XRays [109]. Then, the AMFM estimates of each XRay image is encoded using their histograms as described in the Section 2.4.1 using the tuned bandpass filters and scales showed in Tables 1 and 2. The final classification was computed using the linear regression method PLS (described in Section 2.5).
The results obtained by the system were excellent (area under the ROC curve, AUC = 1.0). However, the significance of the results should be debated based on the small database used. The authors plan as future work the testing of the system using a much bigger database. The authors produced classification results that were significantly better than those presented in [102, 103, 107].
3.4. Carotid artery ultrasound images
Cardiovascular disease (CVD) is the third leading cause of death and adult disability in the industrial world after heart attack and cancer. Of all the deaths caused by CVD among adults aged 20 and older, an estimated 6 millions are attributed to coronary heart disease and to stroke, with atherosclerosis as the underlying cause [80–82, 110].
A method based on image analysis of ultrasound images of carotid plaques that can differentiate between the stable plaques that tend to remain asymptomatic and the unstable ones that eventually produce symptoms has the potential to refine the basis for surgery and spare some patients from an unnecessary costly operation which itself carries a risk of stroke.
AMFM methods are being applied for characterizing and analyzing plaques in ultrasound images. Christodoulou et al. present in [81] their investigations for the AMFM characterization of carotid plaques in ultrasound images. In [82], Loizou et al. present how to use AMFM features for describing atherosclerotic plaque features. In what follows, we described the basics of their approaches.
The extraction of features characterizing efficiently the structure of ultrasound carotid plaques is important for the identification of individuals with asymptomatic carotid stenosis at risk of stroke. Christodoloulou et al. present how to characterize the carotid plaques using AMFM features in [81]. They use as basic descriptors the information about the AMFM estimates similar as in the Section 2.4.1: the IA, IF magnitude and IF angle histograms. In addition to the AMFM features, the authors compute Spatial Gray Level Dependence Matrices (SGLDM) computing the following texture measures: (i) angular second moment, (ii) contrast, (iii) correlation, (iv) sum of squares: variance, (v) inverse difference moment, (vi) sum average, (vii) sum variance, (viii) sum entropy, (ix) entropy, (x) difference variance, (xi) difference entropy and (xii) information measures of correlation. Also, the Gray Level Difference Statistics (GLDS) are computed: (i) contrast, (ii) angular second moment, (iii) entropy and (iv) mean. The final step applied by the authors corresponds to the statistical knearest neighbor (KNN) classifier implemented for different values of k (k = 1, 3, 5, 7, 9, 11, 13). The authors applied their method to a database of 274 carotid plaque ultrasound images divided as 137 symptomatic and 137 asymptomatic. Using the AMFM estimates, the authors got a classification success up to 71.5% when the three AMFM estimates and k = 5 were used. This result was better than using the textures features SGLDM and GLDS that gave 68.2%.
Loizou et al. [82] present in an AMFM analysis as an application for investigating the intima media complex (IMC), media layer (ML) and intima layer (IL) of the common carotid artery (CCA). This study represents the first study for the IMC, IL and ML. Clinically, the intimamedia thickness (IMT) is used as a validated measure for the assessment of atherosclerosis, that causes enlargement of the arteries and thickening of the artery walls. The authors use the same AMFM histograms as in Section 2.4.1 but computed using only horizontaloriented bandpass filters. Thus, the authors use similar scales like those described in Table 1 but using only the filters numbered as (see Figure 2a): 1 (LPF), 2, 5 (in the H scale), 8, 11 (in the M scale) and 14 and 17 (in the L scale). The reason for the selection of these horizontaloriented filters is related with the horizontally elongated nature of the atherosclerotic structures. As the last step for the statistical analysis, the authors use the MannWhitney rank sum test in order to identify is there are significant differences (SD) or not (NS) between the extracted AMFM features. The authors use p < 0.05 for significant differences and comparison between different age groups.
Their study, performed on 100 ultrasound images, reveals that the IA of the media layer decreases with age. The authors state that the decreasing of the IA is maybe related to the reduction in calcified, stable plaque components and an increase in stroke risk with age. In terms of the IF, the median of this AMFM estimate of the media layer increases suggesting fragmentation of solid, large plaque components that also increases the risk of stroke.
4. Conclusions and future work
We have provided a summary of recent AMFM applications in medical imaging. In the coming years, we expect that there will be a variety of new applications. Here, it is important to note that medical imaging applications come from a variety of AMFM methods and models.
The advantages of considering AMFM models come from their ability to describe image structures over different frequency scales. For example, in retinal images, structures such as drusen and microaneurysms have a welldefined shape that get captured by the higherfrequency scale AMFM filters. On the other hand, vessels and hemorrhages are better represented in the lower frequencies. In chest radiographs, nodules can also be well represented using the AMFM features. The combination of feature extraction and classification using PLS has produced robust systems for the analysis of chest radiographs, where an automatic grading system for pneumoconiosis has been demonstrated on a limitedsize database. For DR, a screening system has been developed and it is currently being tested on an extensive database for FDA approval.
Future work on AMFM models will undoubtedly yield new methods and new applications. We expect to see new applications from atleast three separate approaches: (i) applications from AMFM methods associated with multidimensional energy operators, (ii) applications from multiscale AMFM decompositions based on Hilbertbased methods, (iii) applications associated with methods associated with the monogenic signal, and (iv) applications from new AMFM methods that are currently being developed.
Declarations
Authors’ Affiliations
References
 Unser M, Aldroubi A, Laine A: Guest editorial: Wavelets in medical imaging. IEEE Trans Med Imag 2003, 22: 285288. 10.1109/TMI.2003.809638View ArticleGoogle Scholar
 Osareh A, Shadgar B: Retinal vessel extraction using gabor filters and support vector machines. Commun Comput Inf Sci 2009, 6: 356363. 10.1007/9783540899853_44View ArticleGoogle Scholar
 Havlicek JP: AMFM image models. The University of Texas at Austin; 1996.Google Scholar
 Murray Herrera VM: AMFM methods for image and video processing. University of New Mexico; 2008.Google Scholar
 Murray V, Rodriguez P, Pattichis MS: Multiscale AMFM demodulation and image reconstruction methods with improved accuracy. IEEE Trans Image Process 2010, 19(5):11381152.MathSciNetView ArticleGoogle Scholar
 Pattichis MS, Bovik AC: Analyzing image structure by multidimensional frequency modulation. IEEE Trans Pattern Anal Mach Intell 2007, 29(5):753766.View ArticleGoogle Scholar
 Pattichis M, Pattichis C, Avraam M, Bovik A, Kyriacou K: AMFM texture segmentation in electron microscopic muscle imaging. IEEE Trans Med Imag 2000, 19(12):12531257. 10.1109/42.897818View ArticleGoogle Scholar
 Murray V, Pattichis M, Soliz P: New AMFM analysis methods for retinal image characterization. Asilomar Conference on Signals, Systems and Computers 2008.Google Scholar
 Agurto C, Murray V, Barriga E, Murillo S, Pattichis M, Davis H, Russell S, Abramoff M, Soliz P: Multiscale AMFM methods for diabetic retinopathy lesion detection. IEEE Trans Med Imag 2010, 29(2):502512.View ArticleGoogle Scholar
 Pattichis M: Multidimensional AMFM models and methods for biomedical image computing. the 34th IEEE Annual International Conference of the Engineering in Medicine and Biology Society 2009.Google Scholar
 Fleet DJ, Jepson AD: Computation of component image velocity from local phase information. Int J Comput Vision 1990, 5(1):77104. 10.1007/BF00056772View ArticleGoogle Scholar
 Murray V, Pattichis MS: AMFM demodulation methods for reconstruction, analysis and motion estimation in video signals. In IEEE Southwest Symposium on Image Analysis and Interpretation. Volume 0. IEEE Computer Society, Los Alamitos, CA, USA; 2008:1720.Google Scholar
 Murray V, Murillo SE, Pattichis MS, Loizou CP, Pattichis CS, Kyriacou E, Nicolaides A: An AMFM model for motion estimation in atherosclerotic plaque videos. 41st Asilomar Conference on Signals, Systems and Computers 2007, 746750.Google Scholar
 Havlicek J, Tay P, Bovik A: Handbook of Image and Video Processing. Elsevier Academic Press, Ch. AMFM Image Models: Fundamental Techniques and Emerging Trends; 2005:377395.View ArticleGoogle Scholar
 Pattichis M, Bovik A: AMFM expansions for images. Proc European Signal Processing Conference 1996.Google Scholar
 Pattichis M, Bovik A, Havlicek J, Sidiropoulos N: Multidimensional orthogonal fm transforms. IEEE Trans Image Process 2001, 10(3):448464. 10.1109/83.908521MathSciNetMATHView ArticleGoogle Scholar
 Pattichis M, Panayi G, Bovik A, ShunPin H: Fingerprint Classification using an AMFM model. IEEE Trans Image Process 2001, 10(6):951954. 10.1109/83.923291MATHView ArticleGoogle Scholar
 Ramachandran J: Image analysis of wood core using instantaneous wavelength and frequency modulation. University of New Mexico; 2008.Google Scholar
 Kaiser J: On a simple algorithm to calculate the 'energy' of a signal. International Conference on Acoustics, Speech, and Signal Processing 1990, 1: 381384.View ArticleGoogle Scholar
 Kaiser J: On teager's energy algorithm and its generalization to continuous signals. In IEEE Digital Signal Processing Workshop. New Paltz, NY; 1990.Google Scholar
 Kaiser J: Some useful properties of teager's energy operators. IEEE International Conference on Acoustics, Speech, and Signal Processing 1993, 3: 149152.Google Scholar
 Maragos P, Kaiser JF, Quatieri TF: On amplitude and frequency demodulation using energy operators. IEEE Trans Signal Process 1993, 41(4):15321550. 10.1109/78.212729MATHView ArticleGoogle Scholar
 Maragos P, Kaiser JF, Quatieri TF: Energy separation in signal modulations with applications to speech analysis. IEEE Trans Signal Process 1993, 41(10):30243051. 10.1109/78.277799MATHView ArticleGoogle Scholar
 Maragos P, Bovik AC: Image demodulation using multidimensional energy separation. J Opt Soc Am A 1995, 12(9):18671876. 10.1364/JOSAA.12.001867View ArticleGoogle Scholar
 Maragos P, Quatieri T, Kaiser J: Speech nonlinearities, modulations, and energy operators. International Conference on Acoustics, Speech, and Signal Processing 1991, 1: 421424.Google Scholar
 Maragos P, Kaiser J, Quatieri T: On separating amplitude from frequency modulations using energy operators. IEEE International Conference on Acoustics, Speech, and Signal Processing 1992, 2: 14.Google Scholar
 Maragos P, Bovik A, Quatieri T: A multidimensional energy operator for image processing. SPIE Symp Visual Commun Image Processing 1992.Google Scholar
 Bovik A, Gopal N, Emmoth T, Restrepo A: Localized measurement of emergent image frequencies by gabor wavelets. IEEE Trans Inf Theory 1992, 38(2):691712. 10.1109/18.119731View ArticleGoogle Scholar
 Bovik A, Maragos P, Quatieri T: Amfm energy detection and separation in noise using multiband energy operators. IEEE Trans Signal Process 1993, 41(12):32453265. 10.1109/78.258071MATHView ArticleGoogle Scholar
 Maragos P, Bovik A: Demodulation of images modeled by amplitudefrequency modulations using multidimensional energy separation. IEEE International Conference on Image Processing 1994, 3: 421425.View ArticleGoogle Scholar
 Pattichis MS: AMFM transforms with applications. University of Texas at Austin; 1998.Google Scholar
 Kokkinos I, Evangelopoulos G, Maragos P: Texture analysis and segmentation using modulation features, generative models, and weighted curve evolution. IEEE Trans Pattern Anal Mach Intell 2009, 31(1):142157.View ArticleGoogle Scholar
 Havlicek J, Havlicek J, Bovik A: The analytic image. Image Processing, 1997. Proceedings, International Conference on 1997, 2: 446449.Google Scholar
 Havlicek J, Havlicek J, Mamuya N, Bovik A: Skewed 2d hilbert transforms and computed amfm models. Image Processing, 1998. ICIP 98. Proceedings. 1998 International Conference on 1998, 1: 602606.Google Scholar
 Havlicek J, Harding D, Bovik A: Discrete quasieigenfunction approximation for amfm image analysis. Image Processing, 1996. Proceedings, International Conference on 1996, 1: 633636.Google Scholar
 Havlicek J, Harding D, Bovik A: Extracting essential modulated image structure. Signals, Systems and Computers, 1996. 1996 Conference Record of the Thirtieth Asilomar Conference on 1996, 2: 10141018.Google Scholar
 Havlicek J, Bovik A: Multicomponent amfm image models and waveletbased demodulation with component tracking. Image Processing, 1994. Proceedings. ICIP94., IEEE International Conference 1994, 1: 4145.Google Scholar
 Havlicek J, Bovik A, Maragos P: Modulation models for image processing and waveletbased image demodulation. Signals, Systems and Computers, 1992. 1992 Conference Record of The TwentySixth Asilomar Conference on 1992, 2: 805810.View ArticleGoogle Scholar
 Havlicek J, Harding D, Bovik A: The multicomponent amfm image representation. Image Process. IEEE Trans 1996, 5(6):10941100.Google Scholar
 Havlicek J, Pattichis M, Harding D, Christofides A, Bovik A: Amfm image analysis techniques. Image Analysis and Interpretation, 1996., Proceedings of the IEEE Southwest Symposium on 1996, 195200.Google Scholar
 Havlicek J, Harding D, Bovik A: Reconstruction from the multicomponent amfm image representation. Image Processing, 1995. Proceedings, International Conference on 1995, 2: 280283.Google Scholar
 Vakman D: Signals Oscillations and Waves: A Modern Approach. Artech House, Boston; 1998.Google Scholar
 Vakman D: On the Analytic Signal, the TeagerKaiser energy algorithm, and other methods for defining amplitude and frequency. IEEE Trans Signal Process 1996, 44(4):791797. 10.1109/78.492532View ArticleGoogle Scholar
 Girolami G, Vakman D: Instantaneous frequency estimation and measurement: a QuasiLocal Method. Measurement Sci Tech 2002, 13(6):909917. 10.1088/09570233/13/6/312View ArticleGoogle Scholar
 Rodriguez P, Pattichis M: New algorithms for fast and accurate amfm demodulation of digital images. IEEE International Conference on Image Processing 2005, 2: II12947.Google Scholar
 Larkin KG, Bone DJ, Oldfield MA: Natural demodulation of twodimensional fringe patterns. I. General background of the spiral phase quadrature transform. J Opt Soc Amer A: Opt Image Sci Vision 2001, 18(8):18621870. 10.1364/JOSAA.18.001862View ArticleGoogle Scholar
 Larkin KG: Natural demodulation of twodimensional fringe patterns. II. Stationary phase analysis of the spiral phase quadrature transform. J Opt Soc Amer A: Opt Image Sci Vision 2001, 18(8):18711881. 10.1364/JOSAA.18.001871View ArticleGoogle Scholar
 Felsberg M, Sommer G: The Monogenic Signal. IEEE Trans Signal Process 2001, 49(12):31363144. 10.1109/78.969520MathSciNetView ArticleGoogle Scholar
 Felsberg M, Sommer G: The monogenic scalespace: A unifying approach to phasebased image processing in scalespace. J Math Imag Vision 2004, 21: 526.MathSciNetView ArticleGoogle Scholar
 Felsberg M, Sommer G: A new extension of linear signal processing for estimating local properties and detecting features. In 22. DAGM Symposium Mustererkennung 2000, 195202.Google Scholar
 Unser M, Sage D, Van De Ville D: Multiresolution monogenic signal analysis using the rieszlaplace wavelet transform. IEEE Trans Image Process 2009, 18(11):24022418.MathSciNetView ArticleGoogle Scholar
 Mellor M, Hong BW, Brady M: Locally rotation, contrast, and scale invariant descriptors for texture analysis. IEEE Trans Pattern Anal Mach Intell 2008, 30(1):5261.View ArticleGoogle Scholar
 Grau V, Becher H, Noble J: Registration of multiview realtime 3d echocardiographic sequences. IEEE Trans Med Imag 2007, 26(9):11541165.View ArticleGoogle Scholar
 Felsberg M, Köthe U: GET: The connection between monogenic scalespace and gaussian derivatives. In ScaleSpace 2005. Volume 3459. Springer LNCS; 2005:192203.Google Scholar
 Hahn SL: The analytic, quaternionic and monogenic 2D complex delta distributions, report 3, Warsaw University Technology, Institute of Radioelectronics, Nowowiejska. 2002.Google Scholar
 Bülow T, Sommer G: Hypercomplex signals  a novel extension of the analytic signal to the multidimensional case. IEEE Trans Signal Process 2001, 49(11):28442852. 10.1109/78.960432MathSciNetView ArticleGoogle Scholar
 Kothe U, Felsberg M: RieszTransforms vs. Derivatives: On the relationship between the boundary tensor and the energy tensor. In Scale Space and PDE Methods in Computer Vision. Edited by: Kimmel, R, Sochen, N, Weickert, J. Springer; 2005:179191. vol. 3459 of LNCSView ArticleGoogle Scholar
 Knutsson H, Westin CF, Andersson M: Representing local structure using tensors ii. In Image Analysis. Edited by: Heyden, A, Kahl, F. Springer Berlin/Heidelberg; 2011:545556. vol. 6688 of Lecture Notes in Computer ScienceView ArticleGoogle Scholar
 Knutsson H, Loglets AM: Generalized quadrature and phase for local spatiotemporal structure estimation. In Image Analysis. Edited by: Bigun, J, Gustavsson, T. Springer Berlin/Heidelberg; 2003:107108. vol. 2749 of Lecture Notes in Computer ScienceGoogle Scholar
 Knutsson H: Representing local structure using tensors, Tech. rep. Computer Vision Laboratory, Linkoping University; 1989.Google Scholar
 Selesnick I, Baraniuk R, Kingsbury N: The dualtree complex wavelet transform. Signal Process Mag IEEE 2005, 22(6):123151.View ArticleGoogle Scholar
 Kingsbury N: Complex wavelets for shift invariant analysis and filtering of signals. Appl Comput Harmonic Anal 2001, 10(3):234253. 10.1006/acha.2000.0343MathSciNetMATHView ArticleGoogle Scholar
 Kingsbury N: The dualtree complex wavelet transform: A new technique for shift invariance and directional filters. In 8th IEEE DSP Workshop. Bryce Canyon; 1998:319322.Google Scholar
 Kingsbury N: Image processing with complex wavelets. Phil Trans Royal Soc Lond A 1997, 357: 25432560.View ArticleGoogle Scholar
 Olhede S, Metikas G: The monogenic wavelet transform. IEEE Trans Signal Process 2009, 57(9):34263441.MathSciNetView ArticleGoogle Scholar
 Murray V, Rodriguez VP, Pattichis MS: Robust multiscale AMFM demodulation of digital images. IEEE International Conference on Image Processing 2007, 1: 465468.Google Scholar
 Murray V, Pattichis MS, Davis H, Barriga ES, Soliz P: Multiscale AMFM analysis of pneumoconiosis xray images. IEEE International Conference on Image Processing 2009, 42014204.Google Scholar
 Murray V, Pattichis MS, Soliz P: Retrieval of XRay images with different grades of opacities using multiscale amfm methods. Asilomar Conference on Signals, Systems and Computers 2009, 1216.Google Scholar
 International Labour Office: Guidelines for the use of ILO International Classification of Radiographs of Pneumoconioses. Geneva, Switzerland; 1980.Google Scholar
 Hwang H, Haddad R: Adaptive median filters: new algorithms and results. IEEE Trans Image Process 1995, 4(4):499502. 10.1109/83.370679View ArticleGoogle Scholar
 de Jong S: SIMPLS: An alternative approach to partial least squares regression. Chemometr Intell Lab Syst 1993, 18(3):251263. 10.1016/01697439(93)85002XView ArticleGoogle Scholar
 Barker M, Rayens W: Partial least squares for discrimination. J Chemometr 2003, 17(3):166173. 10.1002/cem.785View ArticleGoogle Scholar
 Schonfeld D, Goutsias J: Optimal morphological pattern restoration from noisy binary images. IEEE Trans Pattern Anal Mach Intell 1991, 13(1):1429. 10.1109/34.67627View ArticleGoogle Scholar
 Osman NF, McVeigh ER, Prince JL: Imaging heart motion using harmonic phase mri. IEEE Trans Med Imag 2000, 19(3):186202. 10.1109/42.845177View ArticleGoogle Scholar
 Elshinawy M, Chouikha M: Using amfm image modeling technique in mammograms. MicroNanoMechatronics and Human Science, 2003 IEEE International Symposium on 2003, 2: 660663.Google Scholar
 Elshinawy MY, Zeng J, Lo SCB, Chouikha MF: Breast cancer detection in mammogram with amfm modeling and gabor filtering. Proc 7th International Conference on Signal Processing 2004, 3: 25642567.Google Scholar
 Boudraa AO, Cexus JC, Zaidi H: Functional segmentation of dynamic nuclear images by crossif_{ b }energy operator. Comput Methods Progr Biomed 2006, 84(23):146152. medical Image Segmentation Special Issue 10.1016/j.cmpb.2006.09.002View ArticleGoogle Scholar
 Maragos P, Loupas T, Pitsikalis V: Improving doppler ultrasound spectroscopy with multiband instantaneous energy separation. Proc 14th International Conference on Digital Signal Processing 2002, 2: 611614.Google Scholar
 Alexandratou E, Sofou A, Papasaika H, Maragos P, Yova D, Kavantzas N: Computer vision algorithms in DNA ploidy image analysis. In Proc of the SPIE Imaging, Manipulation, and Analysis ofBiomolecules, Celss, and Tissues. Edited by: Farkas DL, Nicolau DV, Leif RC. SPIE; 2006:180190. vol. 6088 of IVGoogle Scholar
 Christodoulou C, Kaplanis P, Murray V, Pattichis M, Pattichis C: Classification of surface electromyographic signals using AMFM features. In 19th International Conference on Artificial Neural Networks. Limassol, Cyprus; 2009.Google Scholar
 Christodoulou CI, Pattichis C, Murray V, Pattichis M, Nicolaides A: AMFM representations for the characterization of carotid plaque ultrasound images. 4th European Conference of the International Federation for Medical and Biological Engineering 2009, 22: 546549. 10.1007/9783540892083_130View ArticleGoogle Scholar
 Loizou CP, Murray V, Pattichis MS, Christodoulou CS, Pantziaris M, Nicolaides A, Pattichis CS: AMFM texture image analysis of the intima and media layers of the carotid artery. In 19th International Conference on Artificial Neural Networks. Limassol, Cyprus; 2009.Google Scholar
 Loizou C, Murray V, Pattichis M, Pantziaris M, Pattichis C: Multiscale amplitude modulationfrequency modulation (amfm) texture analysis of ultrasound images of the intima and media layers of the carotid artery. IEEE Trans Inf Tech Biomed 2011, 15(2):178188.View ArticleGoogle Scholar
 Acton S, Soliz P, Russell S, Pattichis M: Content based image retrieval: The foundation for future casebased and evidencebased ophthalmology. Proc IEEE International Conference on Multimedia and Expo 2008, 541544.Google Scholar
 Agurto C, Murillo S, Murray V, Pattichis M, Russell S, Abramoff M, Soliz P: Detection and phenotyping of retinal disease using AMFM processing for feature extraction. Asilomar Conference on Signals, Systems and Computers 2008, 659663.Google Scholar
 Barriga E, Murray V, Agurto C, Pattichis M, Russell S, Abramoff M, Davis H, Soliz P: Multiscale AMFM for lesion phenotyping on agerelated macular degeneration. In IEEE International Symposium on ComputerBasedMedical Systems. Albuquerque, New Mexico; 2009.Google Scholar
 Ezzat T, Bouvrie J, Poggio T: AMFM demodulation of spectrograms using localized 2d maxgabor analysis. Proc IEEE International Conference on Acoustics, Speech and Signal Processing ICASSP 2007, 4: IV1061IV1064.Google Scholar
 Gianfelici F, Turchetti C, Crippa P: Multicomponent AMFM demodulation: The state of the art after the development of the iterated hilbert transform. IEEE International Conference on Signal Processing and Communications ICSPC 2007, 14711474.Google Scholar
 Wang N, Ambikairajah E, Celler B, Lovell N: Feature extraction using an AMFM model for gait pattern classification. Proc IEEE Biomedical Circuits and Systems Conference BioCAS 2008, 2528.Google Scholar
 Li H, Fu L, Li Z: Fault detection and diagnosis of gear wear based on teagerhuang transform. Proc InternationalJoint Conference on Artificial Intelligence JCAI '09 2009, 663666.Google Scholar
 Nguyen DP, Barbieri R, Wilson MA, Brown EN: Instantaneous frequency and amplitude modulation of EEG in the hippocampus reveals state dependent temporal structure. Proc 30th Annual International Conference of the IEEE Engineering in Medicine and Biology Society EMBS 2008, 17111715.Google Scholar
 Prakash R, Aravind R: Modulationdomain particle filter for template tracking. Proc 19th International Conference on Pattern Recognition ICPR 2008 2008, 14.Google Scholar
 Senthil PR, Aravind R: Invariance properties of AMFM image features with application to template tracking. Proc Sixth Indian Conference on Computer Vision, Graphics & Image Processing ICVGIP '08 2008, 614620.Google Scholar
 Mould N, Nguyen C, Havlicek J: Infrared target tracking with AMFM consistency checks. Proc IEEE Southwest Symposium on Image Analysis and Interpretation SSIAI 2008 2008, 58.View ArticleGoogle Scholar
 Kokkinos I, Evangelopoulos G, Maragos P: Texture analysis and segmentation using modulation features, generative models, and weighted curve evolution. IEEE Trans Pattern Anal Mach Intell 2009, 31(1):142157.View ArticleGoogle Scholar
 Tay P: AMFM image analysis using the hilbert huang transform. Proc IEEE Southwest Symposium on Image Analysis and Interpretation SSIAI 2008 2008, 1316.View ArticleGoogle Scholar
 Belaid A, Boukerroui D, Maingourd Y, Lerallut JF: Phasebased level set segmentation of ultrasound images. IEEE Trans Inf Tech Biomed 2011, 15(1):138147.View ArticleGoogle Scholar
 Klonoff DC, Schwartz DM: An economic analysis of interventions for diabetes. Diabetes care 2000, 23: 390404. 10.2337/diacare.23.3.390View ArticleGoogle Scholar
 Agurto C, Pattichis M, Murillo S, Murray V, Abramoff M, Russell S, Barriga E, Davis H, Soliz P: Detection of structures in the retina using amfm for diabetic retinopathy classification. 2009 Meeting of the Association for Research in Vision and Ophthalmology 2009.Google Scholar
 TECHNOVISION Project: MESSIDOR: methods to evaluate segmentation and indexing techniques in the field of retinal ophthalmology.[http://messidor.crihan.fr/]
 AREDS, Areds database[http://eyephoto.ophth.wisc.edu/ResearchAreas/AREDS/AREDSstdPhotoIndex.htm]
 Soliz P, Pattichis MS, Ramachandran J, James DS: Computerassisted diagnosis of chest radiographs for pneumoconioses. In SPIE. Volume 4322. Edited by: Sonka, M, Hanson, KM. SPIE; 2001:667675.Google Scholar
 Pattichis M, Pattichis C, Christodoulou C, James D, Ketai L, Soliz P: A screening system for the assessment of opacity profusion in chest radiographs of miners with pneumoconiosis. IEEE Southwest Symposium on Image Analysis and Interpretation 2002, 130133.View ArticleGoogle Scholar
 Kondo H, Kouda T: Detection of pneumoconiosis rounded opacities using neural network. Joint 9th IFSA World Congress and 20th NAFIPS International Conference 2001, 3: 15811585.Google Scholar
 Kondo H, Kouda T: Computeraided diagnosis for pneumoconiosis using neural network. IEEE Symposium on ComputerBased Medical Systems 2001, 467472.Google Scholar
 Pattichis M, Cacoullos T, Soliz P: New models for region of interest reader classification analysis in chest radiographs. Pattern Recogn 2009, 42(6):10581066. digital Image Processing and Pattern Recognition Techniques for the Detection of Cancer 10.1016/j.patcog.2008.09.021View ArticleGoogle Scholar
 Pattichis M, Muralldharan H, Pattichis C, Soliz P: New image processing models for opacity image analysis in chest radiographs. IEEE Southwest Symposium on Image Analysis and Interpretation 2002, 260264.View ArticleGoogle Scholar
 Van Ginneken B, Ter Haar Romeny BM, Viergever M: Computeraided diagnosis in chest radiography: a survey. IEEE Trans Med Imag 2001, 20(12):12281241. 10.1109/42.974918View ArticleGoogle Scholar
 Pattichis M, Ramachandran J, Wilson M, Pattichis C, Soliz P: Optimal scanning, display, and segmentation of the international labor organization (ILO) Xray images set for pneumoconiosis. IEEE Symposium on ComputerBased Medical Systems 2001, 511515.Google Scholar
 Loizou CP, Murray V, Pattichis MM, Seimenis I, Pantziaris M, Pattichis CS: Multiscale amplitudemodulation frequencymodulation (amfm) texture analysis of multiple sclerosis in brain mri images. IEEE Trans Inf Technol Biomed 2011, 15(1):119129.View ArticleGoogle Scholar
 Pitris C, Kartakoullis A, Bousi E: AMFM techniques in the analysis of optical coherence tomography signals. J Biophotonics 2009, 2(67):364369. 10.1002/jbio.200910023View ArticleGoogle Scholar
 Kartakoulis A, Bousi E, Pitris C: AMFM analysis of optical coherence tomography signals. In Optical Coherence Tomography and Coherence Domain Optical Methods in Biomedicine XIII. Volume 7168. Edited by: Fujimoto, JG, Izatt, JA, Tuchin, VV. SPIE; 2009:71681M.View ArticleGoogle Scholar
 Kartakoullis A, Bousi E, Pitris C: AMFM techniques in optical coherence tomography. In Optical Coherence Tomography and Coherence Techniques IV. Volume 7372. Edited by: Andersen, PE, Bouma, BE. SPIE; 2009:73720U.View ArticleGoogle Scholar
 Rodriguez VP, Pattichis MS: Nested random phase sequence sets: a link between AMFM demodulation and increasing operators with application to cardiac image analysis. Proc 6th IEEE Southwest Symposium on Image Analysis and Interpretation 2004, 196200.Google Scholar
 Rodriguez VP, Pattichis MS: Real time AMFM analysis of ultrasound video. 45th Midwest Symposium on Circuits and Systems 2002, 1: I21619.Google Scholar
 Rodriguez VP, Pattichis M, Goens M, Abdallah R: MHealth: Emerging Mobile Health Systems, Springer US. 2006, 491507.View ArticleGoogle Scholar
 Gill D, Gavrieli N, Intrator N: Detection and identification of heart sounds using homomorphic envelogram and selforganizing probabilistic model. Proc Computers in Cardiology 2005, 957960.Google Scholar
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