Invariant scattering convolution networks

Cascaded Amplitude Modulations in Sound Texture Perception

Sound textures, such as crackling fire or chirping crickets, represent a broad class of sounds defined by their homogeneous temporal structure. It has been suggested that the perception of texture is mediated by time-averaged summary statistics measured from early auditory representations. In this study, we investigated the perception of sound textures that contain rhythmic structure, specifically second-order amplitude modulations that arise from the interaction of different modulation rates, previously described as “beating” in the envelope-frequency domain. We developed an auditory texture model that utilizes a cascade of modulation filterbanks that capture the structure of simple rhythmic patterns. The model was examined in a series of psychophysical listening experiments using synthetic sound textures—stimuli generated using time-averaged statistics measured from real-world textures. In a texture identification task, our results indicated that second-order amplitude modulation sensitivity enhanced recognition. Next, we examined the contribution of the second-order modulation analysis in a preference task, where the proposed auditory texture model was preferred over a range of model deviants that lacked second-order modulation rate sensitivity. Lastly, the discriminability of textures that included second-order amplitude modulations appeared to be perceived using a time-averaging process. Overall, our results demonstrate that the inclusion of second-order modulation analysis generates improvements in the perceived quality of synthetic textures compared to the first-order modulation analysis considered in previous approaches.

The Incremental Multiresolution Matrix Factorization Algorithm

Multiresolution analysis and matrix factorization are foundational tools in computer vision. In this work, we study the interface between these two distinct topics and obtain techniques to uncover hierarchical block structure in symmetric matrices - an important aspect in the success of many vision problems. Our new algorithm, the incremental multiresolution matrix factorization, uncovers such structure one feature at a time, and hence scales well to large matrices. We describe how this multiscale analysis goes much farther than what a direct "global" factorization of the data can identify. We evaluate the efficacy of the resulting factorizations for relative leveraging within regression tasks using medical imaging data. We also use the factorization on representations learned by popular deep networks, providing evidence of their ability to infer semantic relationships even when they are not explicitly trained to do so. We show that this algorithm can be used as an exploratory tool to improve the network architecture, and within numerous other settings in vision.

Deep scattering convolution network based features for ultrasonic fatty liver tissue characterization

Accumulation of excess fat in the liver tissue is the leading cause for dysfunction of liver, which can lead to the diseases from fibrosis to end stage cirrhosis. Hence, early detection of fatty liver becomes crucial in avoiding the liver from permanent failure. Depending on the concentration of fat in the tissue, the liver is classified as Normal, Grade 1, Grade 2 and Grade 3 respectively. The texture of liver tissue in ultrasound image is so specific to the concentration of fat, hence classifying the fatty liver is formulated as a texture discrimination problem. In this paper, we present an automated algorithm for grading the tissue of a fatty liver based on the features obtained from the invariant scattering convolution network (ISCN). ISCN, which involves cascade of modulus complex wavelet transforms and averaging operations results in scattering coefficients (SC), these coefficients will give stable invariant representations and also maps the texture of fatty liver image to a discriminative manifold giving good features for classification. SC are of high dimension and hence a compact representation feature is obtained by summing all the SC coefficients. Summed SC features along with cubic SVM classifier gave an accuracy of 96.6% in automatically categorizing the fatty content present in the tissue of a liver.

3D scattering transforms for disease classification in neuroimaging

Classifying neurodegenerative brain diseases in MRI aims at correctly assigning discrete labels to MRI scans. Such labels usually refer to a diagnostic decision a learner infers based on what it has learned from a training sample of MRI scans. Classification from MRI voxels separately typically does not provide independent evidence towards or against a class; the information relevant for classification is only present in the form of complicated multivariate patterns (or “features”). Deep learning solves this problem by learning a sequence of non-linear transformations that result in feature representations that are better suited to classification. Such learned features have been shown to drastically outperform hand-engineered features in computer vision and audio analysis domains. However, applying the deep learning approach to the task of MRI classification is extremely challenging, because it requires a very large amount of data which is currently not available. We propose to instead use a three dimensional scattering transform, which resembles a deep convolutional neural network but has no learnable parameters. Furthermore, the scattering transform linearizes diffeomorphisms (due to e.g. residual anatomical variability in MRI scans), making the different disease states more easily separable using a linear classifier. In experiments on brain morphometry in Alzheimer's disease, and on white matter microstructural damage in HIV, scattering representations are shown to be highly effective for the task of disease classification. For instance, in semi-supervised learning of progressive versus stable MCI, we reach an accuracy of 82.7%. We also present a visualization method to highlight areas that provide evidence for or against a certain class, both on an individual and group level.

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We have developed and implemented a feature extraction method based on the three dimensional (3D) scattering transform.

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We tested it for its ability to discriminate diseased from healthy subjects and subjects with mild cognitive impairment.

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We have clearly shown that our proposed methodology achieves higher accuracy than the best competing methods.

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The scattering transform linearizes diffeomorphisms leading to more separable disease states using a linear classifier.

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Scattering representations are shown to be highly effective for the task of disease classification.

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We present a visualization method to highlight areas that provide evidence for or against a certain class.

Deep Learning

Deep learning is a branch of machine learning that tries to model high-level abstractions of data using multiple layers of neurons consisting of complex structures or non-liner transformations. With the increase of the amount of data and the power of computation, neural networks with more complex structures have attracted widespread attention and been applied to various fields. This paper provides an overview of deep learning in neural networks including popular architecture models and training algorithms.

Assessing the utility of autofluorescence-based pulmonary optical endomicroscopy to predict the malignant potential of solitary pulmonary nodules in humans

Solitary pulmonary nodules are common, often incidental findings on chest CT scans. The investigation of pulmonary nodules is time-consuming and often leads to protracted follow-up with ongoing radiological surveillance, however, clinical calculators that assess the risk of the nodule being malignant exist to help in the stratification of patients. Furthermore recent advances in interventional pulmonology include the ability to both navigate to nodules and also to perform autofluorescence endomicroscopy. In this study we assessed the efficacy of incorporating additional information from label-free fibre-based optical endomicrosopy of the nodule on assessing risk of malignancy. Using image analysis and machine learning approaches, we find that this information does not yield any gain in predictive performance in a cohort of patients. Further advances with pulmonary endomicroscopy will require the addition of molecular tracers to improve information from this procedure.

Dynamic Reweighting of Auditory Modulation Filters

Sound waveforms convey information largely via amplitude modulations (AM). A large body of experimental evidence has provided support for a modulation (bandpass) filterbank. Details of this model have varied over time partly reflecting different experimental conditions and diverse datasets from distinct task strategies, contributing uncertainty to the bandwidth measurements and leaving important issues unresolved. We adopt here a solely data-driven measurement approach in which we first demonstrate how different models can be subsumed within a common 'cascade' framework, and then proceed to characterize the cascade via system identification analysis using a single stimulus/task specification and hence stable task rules largely unconstrained by any model or parameters. Observers were required to detect a brief change in level superimposed onto random level changes that served as AM noise; the relationship between trial-by-trial noisy fluctuations and corresponding human responses enables targeted identification of distinct cascade elements. The resulting measurements exhibit a dynamic complex picture in which human perception of auditory modulations appears adaptive in nature, evolving from an initial lowpass to bandpass modes (with broad tuning, Q∼1) following repeated stimulus exposure.

Understanding deep convolutional networks

Deep convolutional networks provide state-of-the-art classifications and regressions results over many high-dimensional problems. We review their architecture, which scatters data with a cascade of linear filter weights and nonlinearities. A mathematical framework is introduced to analyse their properties. Computations of invariants involve multiscale contractions with wavelets, the linearization of hierarchical symmetries and sparse separations. Applications are discussed.

A Mathematical Motivation for Complex-Valued Convolutional Networks

A complex-valued convolutional network (convnet) implements the repeated application of the following composition of three operations, recursively applying the composition to an input vector of nonnegative real numbers: (1) convolution with complex-valued vectors, followed by (2) taking the absolute value of every entry of the resulting vectors, followed by (3) local averaging. For processing real-valued random vectors, complex-valued convnets can be viewed as data-driven multiscale windowed power spectra, data-driven multiscale windowed absolute spectra, data-driven multiwavelet absolute values, or (in their most general configuration) data-driven nonlinear multiwavelet packets. Indeed, complex-valued convnets can calculate multiscale windowed spectra when the convnet filters are windowed complex-valued exponentials. Standard real-valued convnets, using rectified linear units (ReLUs), sigmoidal (e.g., logistic or tanh) nonlinearities, or max pooling, for example, do not obviously exhibit the same exact correspondence with data-driven wavelets (whereas for complex-valued convnets, the correspondence is much more than just a vague analogy). Courtesy of the exact correspondence, the remarkably rich and rigorous body of mathematical analysis for wavelets applies directly to (complex-valued) convnets.

The Radon Cumulative Distribution Transform and Its Application to Image Classification

Invertible image representation methods (transforms) are routinely employed as low-level image processing operations based on which feature extraction and recognition algorithms are developed. Most transforms in current use (e.g., Fourier, wavelet, and so on) are linear transforms and, by themselves, are unable to substantially simplify the representation of image classes for classification. Here, we describe a nonlinear, invertible, low-level image processing transform based on combining the well-known Radon transform for image data, and the 1D cumulative distribution transform proposed earlier. We describe a few of the properties of this new transform, and with both theoretical and experimental results show that it can often render certain problems linearly separable in a transform space.

PCANet: A Simple Deep Learning Baseline for Image Classification?

In this paper, we propose a very simple deep learning network for image classification that is based on very basic data processing components: 1) cascaded principal component analysis (PCA); 2) binary hashing; and 3) blockwise histograms. In the proposed architecture, the PCA is employed to learn multistage filter banks. This is followed by simple binary hashing and block histograms for indexing and pooling. This architecture is thus called the PCA network (PCANet) and can be extremely easily and efficiently designed and learned. For comparison and to provide a better understanding, we also introduce and study two simple variations of PCANet: 1) RandNet and 2) LDANet. They share the same topology as PCANet, but their cascaded filters are either randomly selected or learned from linear discriminant analysis. We have extensively tested these basic networks on many benchmark visual data sets for different tasks, including Labeled Faces in the Wild (LFW) for face verification; the MultiPIE, Extended Yale B, AR, Facial Recognition Technology (FERET) data sets for face recognition; and MNIST for hand-written digit recognition. Surprisingly, for all tasks, such a seemingly naive PCANet model is on par with the state-of-the-art features either prefixed, highly hand-crafted, or carefully learned [by deep neural networks (DNNs)]. Even more surprisingly, the model sets new records for many classification tasks on the Extended Yale B, AR, and FERET data sets and on MNIST variations. Additional experiments on other public data sets also demonstrate the potential of PCANet to serve as a simple but highly competitive baseline for texture classification and object recognition.

On Statistical Analysis of Neuroimages with Imperfect Registration

A variety of studies in neuroscience/neuroimaging seek to perform statistical inference on the acquired brain image scans for diagnosis as well as understanding the pathological manifestation of diseases. To do so, an important first step is to register (or co-register) all of the image data into a common coordinate system. This permits meaningful comparison of the intensities at each voxel across groups (e.g., diseased versus healthy) to evaluate the effects of the disease and/or use machine learning algorithms in a subsequent step. But errors in the underlying registration make this problematic, they either decrease the statistical power or make the follow-up inference tasks less effective/accurate. In this paper, we derive a novel algorithm which offers immunity to local errors in the underlying deformation field obtained from registration procedures. By deriving a deformation invariant representation of the image, the downstream analysis can be made more robust as if one had access to a (hypothetical) far superior registration procedure. Our algorithm is based on recent work on scattering transform. Using this as a starting point, we show how results from harmonic analysis (especially, non-Euclidean wavelets) yields strategies for designing deformation and additive noise invariant representations of large 3-D brain image volumes. We present a set of results on synthetic and real brain images where we achieve robust statistical analysis even in the presence of substantial deformation errors; here, standard analysis procedures significantly under-perform and fail to identify the true signal.

Construction of An Unbiased Spatio-Temporal Atlas of the Tongue During Speech

Quantitative characterization and comparison of tongue motion during speech and swallowing present fundamental challenges because of striking variations in tongue structure and motion across subjects. A reliable and objective description of the dynamics tongue motion requires the consistent integration of inter-subject variability to detect the subtle changes in populations. To this end, in this work, we present an approach to constructing an unbiased spatio-temporal atlas of the tongue during speech for the first time, based on cine-MRI from twenty two normal subjects. First, we create a common spatial space using images from the reference time frame, a neutral position, in which the unbiased spatio-temporal atlas can be created. Second, we transport images from all time frames of all subjects into this common space via the single transformation. Third, we construct atlases for each time frame via groupwise diffeomorphic registration, which serves as the initial spatio-temporal atlas. Fourth, we update the spatio-temporal atlas by realigning each time sequence based on the Lipschitz norm on diffeomorphisms between each subject and the initial atlas. We evaluate and compare different configurations such as similarity measures to build the atlas. Our proposed method permits to accurately and objectively explain the main pattern of tongue surface motion.

Feature-based Lucas-Kanade and active appearance models

Lucas-Kanade and active appearance models are among the most commonly used methods for image alignment and facial fitting, respectively. They both utilize nonlinear gradient descent, which is usually applied on intensity values. In this paper, we propose the employment of highly descriptive, densely sampled image features for both problems. We show that the strategy of warping the multichannel dense feature image at each iteration is more beneficial than extracting features after warping the intensity image at each iteration. Motivated by this observation, we demonstrate robust and accurate alignment and fitting performance using a variety of powerful feature descriptors. Especially with the employment of histograms of oriented gradient and scale-invariant feature transform features, our method significantly outperforms the current state-of-the-art results on in-the-wild databases.

DERF: distinctive efficient robust features from the biological modeling of the P ganglion cells

Studies in neuroscience and biological vision have shown that the human retina has strong computational power, and its information representation supports vision tasks on both ventral and dorsal pathways. In this paper, a new local image descriptor, termed distinctive efficient robust features (DERF), is derived by modeling the response and distribution properties of the parvocellular-projecting ganglion cells in the primate retina. DERF features exponential scale distribution, exponential grid structure, and circularly symmetric function difference of Gaussian (DoG) used as a convolution kernel, all of which are consistent with the characteristics of the ganglion cell array found in neurophysiology, anatomy, and biophysics. In addition, a new explanation for local descriptor design is presented from the perspective of wavelet tight frames. DoG is naturally a wavelet, and the structure of the grid points array in our descriptor is closely related to the spatial sampling of wavelets. The DoG wavelet itself forms a frame, and when we modulate the parameters of our descriptor to make the frame tighter, the performance of the DERF descriptor improves accordingly. This is verified by designing a tight frame DoG, which leads to much better performance. Extensive experiments conducted in the image matching task on the multiview stereo correspondence data set demonstrate that DERF outperforms state of the art methods for both hand-crafted and learned descriptors, while remaining robust and being much faster to compute.

A learning framework for age rank estimation based on face images with scattering transform

This paper presents a cost-sensitive ordinal hyperplanes ranking algorithm for human age estimation based on face images. The proposed approach exploits relative-order information among the age labels for rank prediction. In our approach, the age rank is obtained by aggregating a series of binary classification results, where cost sensitivities among the labels are introduced to improve the aggregating performance. In addition, we give a theoretical analysis on designing the cost of individual binary classifier so that the misranking cost can be bounded by the total misclassification costs. An efficient descriptor, scattering transform, which scatters the Gabor coefficients and pooled with Gaussian smoothing in multiple layers, is evaluated for facial feature extraction. We show that this descriptor is a generalization of conventional bioinspired features and is more effective for face-based age inference. Experimental results demonstrate that our method outperforms the state-of-the-art age estimation approaches.