AM-FM Analysis of Structural and Functional Magnetic Resonance Images

This thesis proposes the application of multi-dimensional Amplitude-Modulation Frequency-Modulation (AM-FM) methods to magnetic resonance images (MRI). The basic goal is to provide a framework for exploring non-stationary characteristics of structural and functional MRI (sMRI and fMRI). First, we provide a comparison framework for the most popular AM-FM methods using different filterbank configurations that includes Gabor, Equirriple and multi-scale directional designs. We compare the performance and robustness to Gaussian noise using synthetic FM image examples. We show that the multi-dimensional quasi-local method (QLM) with an equiripple filterbank gave the best results in terms of instantaneous frequency (IF) estimation. We then apply the best performing AM-FM method to sMRI to compute the 3D IF features. We use a t-test on the IF magnitude for each voxel to find evidence of significant differences between healthy controls and patients diagnosed with schizophrenia (n=353) can be found in the IF. We also propose the use of the instantaneous phase (IP) as a new feature for analyzing fMRI images. Using principal component analysis and independent component analysis on the instantaneous phase from fMRI, we built spatial maps and identified brain regions that are biologically coherent with the task performed by the subject. This thesis provides the first application of AM-FM models to fMRI and sMRI

Human Attention Detection Using AM-FM Representations

Human activity detection from digital videos presents many challenges to the computer vision and image processing communities. Recently, many methods have been developed to detect human activities with varying degree of success. Yet, the general human activity detection problem remains very challenging, especially when the methods need to work “in the wild” (e.g., without having precise control over the imaging geometry). The thesis explores phase-based solutions for (i) detecting faces, (ii) back of the heads, (iii) joint detection of faces and back of the heads, and (iv) whether the head is looking to the left or the right, using standard video cameras without any control on the imaging geometry. The proposed phase-based approach is based on the development of simple and robust methods that relie on the use of Amplitude Modulation - Frequency Modulation (AM-FM) models. The approach is validated using video frames extracted from the Advancing Outof- school Learning in Mathematics and Engineering (AOLME) project. The dataset consisted of 13,265 images from ten students looking at the camera, and 6,122 images from five students looking away from the camera. For the students facing the camera, the method was able to correctly classify 97.1% of them looking to the left and 95.9% of them looking to the right. For the students facing the back of the camera, the method was able to correctly classify 87.6% of them looking to the left and 93.3% of them looking to the right. The results indicate that AM-FM based methods hold great promise for analyzing human activity videos

AM-FM methods for image and video processing

This dissertation is focused on the development of robust and efficient Amplitude-Modulation Frequency-Modulation (AM-FM) demodulation methods for image and video processing (there is currently a patent pending that covers the AM-FM methods and applications described in this dissertation). The motivation for this research lies in the wide number of image and video processing applications that can significantly benefit from this research. A number of potential applications are developed in the dissertation. First, a new, robust and efficient formulation for the instantaneous frequency (IF) estimation: a variable spacing, local quadratic phase method (VS-LQP) is presented. VS-LQP produces much more accurate results than current AM-FM methods. At significant noise levels (SNR \u3c 30dB), for single component images, the VS-LQP method produces better IF estimation results than methods using a multi-scale filterbank. At low noise levels (SNR \u3e 50dB), VS-LQP performs better when used in combination with a multi-scale filterbank. In all cases, VS-LQP outperforms the Quasi-Eigen Approximation algorithm by significant amounts (up to 20dB). New least squares reconstructions using AM-FM components from the input signal (image or video) are also presented. Three different reconstruction approaches are developed: (i) using AM-FM harmonics, (ii) using AM-FM components extracted from different scales and (iii) using AM-FM harmonics with the output of a low-pass filter. The image reconstruction methods provide perceptually lossless results with image quality index values bigger than 0.7 on average. The video reconstructions produced image quality index values, frame by frame, up to more than 0.7 using AM-FM components extracted from different scales. An application of the AM-FM method to retinal image analysis is also shown. This approach uses the instantaneous frequency magnitude and the instantaneous amplitude (IA) information to provide image features. The new AM-FM approach produced ROC area of 0.984 in classifying Risk 0 versus Risk 1, 0.95 in classifying Risk 0 versus Risk 2, 0.973 in classifying Risk 0 versus Risk 3 and 0.95 in classifying Risk 0 versus all images with any sign of Diabetic Retinopathy. An extension of the 2D AM-FM demodulation methods to three dimensions is also presented. New AM-FM methods for motion estimation are developed. The new motion estimation method provides three motion estimation equations per channel filter (AM, IF motion equations and a continuity equation). Applications of the method in motion tracking, trajectory estimation and for continuous-scale video searching are demonstrated. For each application, we discuss the advantages of the AM-FM methods over current approaches

The Importance of the Instantaneous Phase in Detecting Faces with Convolutional Neural Networks

Convolutional Neural Networks (CNN) have provided new and accurate methods for processing digital images and videos. Yet, training CNNs is extremely demanding in terms of computational resources. Also, for simple applications, the standard use of transfer learning also tends to require far more resources than what may be needed. Furthermore, the final systems tend to operate as black boxes that are difficult to interpret. The current thesis considers the problem of detecting faces from the AOLME video dataset. The AOLME dataset consists of a large video collection of group interactions that are recorded in unconstrained classroom environments. For the thesis, still image frames were extracted at every minute from 18 24-minute videos. Then, each video frame was divided into 9x5 blocks with 50x50 pixels each. For each of the 19440 blocks, the percentage of face pixels was set as ground truth. Face detection was then defined as a regression problem for determining the face pixel percentage for each block. For testing different methods, 12 videos were used for training and validation. The remaining 6 videos were used for testing. The thesis examines the impact of using the instantaneous phase for the AOLME block-based face detection application. For comparison, the thesis compares the use of the Frequency modulation image based on the instantaneous phase, the use of the instantaneous amplitude, and the original gray scale image. To generate the FM and AM inputs, the thesis uses dominant component analysis that aims to decrease the training overhead while maintaining interpretability. The results indicate that the use of the FM image yielded about the same performance as the MobileNet V2 architecture (AUC of 0.78 vs 0.79), with vastly reduced training times. Training was 7x faster for an Intel Xeon with a GTX 1080 based desktop and 11x faster on a laptop with Intel i5 with a GTX 1050. Furthermore, the proposed architecture trains 123x less parameters than what is needed for MobileNet V2. The FM-based neural network architecture uses a single convolutional layer. In comparison, the full LeNet-5 on the same image block using the original image could not be trained for face detection (AUC of 0.5)

The Importance of the Instantaneous Phase in Detecting Faces with Convolutional Neural Networks

Convolutional Neural Networks (CNN) have provided new and accurate methods for processing digital images and videos. Yet, training CNNs is extremely demanding in terms of computational resources. Also, for specific applications, the standard use of transfer learning also tends to require far more resources than what may be needed. Furthermore, the final systems tend to operate as black boxes that are difficult to interpret. The current thesis considers the problem of detecting faces from the AOLME video dataset. The AOLME dataset consists of a large video collection of group interactions that are recorded in unconstrained classroom environments. For the thesis, still image frames were extracted at every minute from 18 24-minute videos. Then, each video frame was divided into 9x5 blocks with 50x50 pixels each. For each of the 19440 blocks, the percentage of face pixels was set as ground truth. Face detection was then defined as a regression problem for determining the face pixel percentage for each block. For testing different methods, 12 videos were used for training and validation. The remaining 6 videos were used for testing. The thesis examines the impact of using the instantaneous phase for the AOLME block-based face detection application. For comparison, the thesis compares the use of the Frequency Modulation image based on the instantaneous phase, the use of the instantaneous amplitude, and the original gray scale image. To generate the FM and AM inputs, the thesis uses dominant component analysis that aims to decrease the training overhead while maintaining interpretability.Comment: Master Thesi

Vector extension of monogenic wavelets for geometric representation of color images

14 pagesInternational audienceMonogenic wavelets offer a geometric representation of grayscale images through an AM/FM model allowing invariance of coefficients to translations and rotations. The underlying concept of local phase includes a fine contour analysis into a coherent unified framework. Starting from a link with structure tensors, we propose a non-trivial extension of the monogenic framework to vector-valued signals to carry out a non marginal color monogenic wavelet transform. We also give a practical study of this new wavelet transform in the contexts of sparse representations and invariant analysis, which helps to understand the physical interpretation of coefficients and validates the interest of our theoretical construction

Multirate Frequency Transformations: Wideband AM-FM Demodulation with Applications to Signal Processing and Communications

The AM-FM (amplitude & frequency modulation) signal model finds numerous applications in image processing, communications, and speech processing. The traditional approaches towards demodulation of signals in this category are the analytic signal approach, frequency tracking, or the energy operator approach. These approaches however, assume that the amplitude and frequency components are slowly time-varying, e.g., narrowband and incur significant demodulation error in the wideband scenarios. In this thesis, we extend a two-stage approach towards wideband AM-FM demodulation that combines multirate frequency transformations (MFT) enacted through a combination of multirate systems with traditional demodulation techniques, e.g., the Teager-Kasiser energy operator demodulation (ESA) approach to large wideband to narrowband conversion factors. The MFT module comprises of multirate interpolation and heterodyning and converts the wideband AM-FM signal into a narrowband signal, while the demodulation module such as ESA demodulates the narrowband signal into constituent amplitude and frequency components that are then transformed back to yield estimates for the wideband signal. This MFT-ESA approach is then applied to the various problems of: (a) wideband image demodulation and fingerprint demodulation, where multidimensional energy separation is employed, (b) wideband first-formant demodulation in vowels, and (c) wideband CPM demodulation with partial response signaling, to demonstrate its validity in both monocomponent and multicomponent scenarios as an effective multicomponent AM-FM signal demodulation and analysis technique for image processing, speech processing, and communications based applications

Modulation Domain Image Processing

The classical Fourier transform is the cornerstone of traditional linearsignal and image processing. The discrete Fourier transform (DFT) and thefast Fourier transform (FFT) in particular led toprofound changes during the later decades of the last century in howwe analyze and process 1D and multi-dimensional signals.The Fourier transform represents a signal as an infinite superpositionof stationary sinusoids each of which has constant amplitude and constantfrequency. However, many important practical signals such as radar returnsand seismic waves are inherently nonstationary. Hence, more complextechniques such as the windowed Fourier transform and the wavelet transformwere invented to better capture nonstationary properties of these signals.In this dissertation, I studied an alternative nonstationary representationfor images, the 2D AM-FM model. In contrast to thestationary nature of the classical Fourier representation, the AM-FM modelrepresents an image as a finite sum of smoothly varying amplitudesand smoothly varying frequencies. The model has been applied successfullyin image processing applications such as image segmentation, texture analysis,and target tracking. However, these applications are limitedto \emph{analysis}, meaning that the computed AM and FM functionsare used as features for signal processing tasks such as classificationand recognition. For synthesis applications, few attempts have been madeto synthesize the original image from the AM and FM components. Nevertheless,these attempts were unstable and the synthesized results contained artifacts.The main reason is that the perfect reconstruction AM-FM image model waseither unavailable or unstable. Here, I constructed the first functionalperfect reconstruction AM-FM image transform that paves the way for AM-FMimage synthesis applications. The transform enables intuitive nonlinearimage filter designs in the modulation domain. I showed that these filtersprovide important advantages relative to traditional linear translation invariant filters.This dissertation addresses image processing operations in the nonlinearnonstationary modulation domain. In the modulation domain, an image is modeledas a sum of nonstationary amplitude modulation (AM) functions andnonstationary frequency modulation (FM) functions. I developeda theoretical framework for high fidelity signal and image modeling in themodulation domain, constructed an invertible multi-dimensional AM-FMtransform (xAMFM), and investigated practical signal processing applicationsof the transform. After developing the xAMFM, I investigated new imageprocessing operations that apply directly to the transformed AM and FMfunctions in the modulation domain. In addition, I introduced twoclasses of modulation domain image filters. These filters produceperceptually motivated signal processing results that are difficult orimpossible to obtain with traditional linear processing or spatial domainnonlinear approaches. Finally, I proposed three extensions of the AM-FMtransform and applied them in image analysis applications.The main original contributions of this dissertation include the following.- I proposed a perfect reconstruction FM algorithm. I used aleast-squares approach to recover the phase signal from itsgradient. In order to allow perfect reconstruction of the phase function, Ienforced an initial condition on the reconstructed phase. The perfectreconstruction FM algorithm plays a critical role in theoverall AM-FM transform.- I constructed a perfect reconstruction multi-dimensional filterbankby modifying the classical steerable pyramid. This modified filterbankensures a true multi-scale multi-orientation signal decomposition. Such adecomposition is required for a perceptually meaningful AM-FM imagerepresentation.- I rotated the partial Hilbert transform to alleviate ripplingartifacts in the computed AM and FM functions. This adjustment results inartifact free filtering results in the modulation domain.- I proposed the modulation domain image filtering framework. Iconstructed two classes of modulation domain filters. I showed that themodulation domain filters outperform traditional linear shiftinvariant (LSI) filters qualitatively and quantitatively in applicationssuch as selective orientation filtering, selective frequency filtering,and fundamental geometric image transformations.- I provided extensions of the AM-FM transform for image decompositionproblems. I illustrated that the AM-FM approach can successfullydecompose an image into coherent components such as textureand structural components.- I investigated the relationship between the two prominentAM-FM computational models, namely the partial Hilbert transformapproach (pHT) and the monogenic signal. The established relationshiphelps unify these two AM-FM algorithms.This dissertation lays a theoretical foundation for future nonlinearmodulation domain image processing applications. For the first time, onecan apply modulation domain filters to images to obtain predictableresults. The design of modulation domain filters is intuitive and simple,yet these filters produce superior results compared to those of pixeldomain LSI filters. Moreover, this dissertation opens up other research problems.For instance, classical image applications such as image segmentation andedge detection can be re-formulated in the modulation domain setting.Modulation domain based perceptual image and video quality assessment andimage compression are important future application areas for the fundamentalrepresentation results developed in this dissertation