Topographic mapping in planetary environments relies on accurate 3D scan registration methods. However, most global registration algorithms relying on features such as FPFH and Harris-3D show poor alignment accuracy in these settings due to the poor structure of the Mars-like terrain and variable resolution, occluded, sparse range data that is hard to register without some a-priori knowledge of the environment. In this paper, we propose an alternative approach to 3D scan registration using the curvelet transform that performs multi-resolution geometric analysis to obtain a set of coefficients indexed by scale (coarsest to finest), angle and spatial position. Features are detected in the curvelet domain to take advantage of the directional selectivity of the transform. A descriptor is computed for each feature by calculating the 3D spatial histogram of the image gradients, and nearest neighbor based matching is used to calculate the feature correspondences. Correspondence rejection using Random Sample Consensus identifies inliers, and a locally optimal Singular Value Decomposition-based estimation of the rigid-body transformation aligns the laser scans given the re-projected correspondences in the metric space. Experimental results on a publicly available data-set of planetary analogue indoor facility, as well as simulated and real-world scans from Neptec Design Group's IVIGMS 3D laser rangefinder at the outdoor CSA Mars yard demonstrates improved performance over existing methods in the challenging sparse Mars-like terrain.
Frequency-domain based approaches decouple the problem of finding rotation and translation transformation parameters and attempt to find a suitable registration in the transformed domain @cite_17 @cite_50 @cite_26 . Phase correlation is typically employed for matching which is robust to the effects of noise and occlusions, while fast Fourier transforms (FFT) used to compute cross-correlations makes this approach computationally efficient. However, the Fourier transform can only retrieve the global frequency content of the signal and provides a dense representation of the underlying signal.
@cite_26 @cite_50 @cite_17
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We present Spectral Registration with Multilayer Resampling (SRMR) as a 6 Degrees Of Freedom (DOF) registration method for noisy 3D data with partial overlap. The algorithm is based on decoupling 3D rotation from 3D translation by a corresponding resampling process of the spectral magnitude of a 3D Fast Fourier Transform (FFT) calculation on discretized 3D range data. The registration of all 6DOF is then subsequently carried out with spectral registrations using Phase Only Matched Filtering (POMF). There are two main aspects for the fast and robust registration of Euler angles from spherical information in SRMR. First of all, there is the permanent use of phase matching. Second, based on the FFT on a discrete Cartesian grid, not only one spherical layer but also a complete stack of layers are processed in one step. Experiments are presented with challenging datasets with respect to interference and overlap. The results include the fast and robust registration of artificially transformed data for ground-truth comparison, scans from the Stanford Bunny dataset, high end 3D laser range finder (LRF) scans of a city center, and range data from a low-cost actuated LRF in a disaster response scenario. This work introduces an original method for registering pairs of 3D views consisting of range data sets which operates in the frequency domain. The Fourier transform allows the decoupling of the estimate of the rotation parameters from the estimate of the translation parameters, our algorithm exploits this well-known property by suggesting a three-step procedure. The rotation parameters are estimated by the first two steps through convenient representations and projections of the Fourier transforms' magnitudes and the translational displacement is recovered by the third step by means of a standard phase correlation technique after compensating one of the two views for rotation. The performance of the algorithm, which is well-suited for unsupervised registration, is clearly assessed through extensive testing with several objects and shows that good and robust estimates of 3D rigid motion are achievable. Our algorithm can be used as a prealignment tool for more accurate space-domain registration techniques, like the ICP algorithm. This correspondence discusses an extension of the well-known phase correlation technique to cover translation, rotation, and scaling. Fourier scaling properties and Fourier rotational properties are used to find scale and rotational movement. The phase correlation technique determines the translational movement. This method shows excellent robustness against random noise. Motion estimation and compensation in wavelet domain have received much attention recently. To overcome the inefficiency of motion estimation in critically sampled wavelet domain, the low-band-shift (LBS) method and the complete-to-overcomplete discrete wavelet transform (CODWT) method are proposed for motion estimation in shift-invariant wavelet domain. However, a major disadvantage of these methods is the computational complexity. Although the CODWT method has reduced the computational complexity by skipping the inverse wavelet transform and making the direct link between the critically sampled subbands and the shift-invariant subbands, the full search algorithm (FSA) increases it. In this paper, we proposed two fast multiresolution motion estimation algorithms in shift-invariant wavelet domain: one is the wavelet matching error characteristic based partial distortion search (WMEC-PDS) algorithm, which improves computational efficiency of conventional partial distortion search algorithms while keeping the same estimate accuracy as the FSA; another is the anisotropic double cross search (ADCS) algorithm using multiresolution-spatio-temporal context, which provides a significantly computational load reduction while only introducing negligible distortion compared with the FSA. Due to the multiresolution nature, both the proposed approaches can be applied to wavelet-based scalable video coding. Experimental results show the superiority of the proposed fast motion estimation algorithms against other fast algorithms in terms of speed-up and quality. This paper proposes an end-to-end approach for single-channel speaker-independent multi-speaker speech separation, where time-frequency (T-F) masking, the short-time Fourier transform (STFT), and its inverse are represented as layers within a deep network. Previous approaches, rather than computing a loss on the reconstructed signal, used a surrogate loss based on the target STFT magnitudes. This ignores reconstruction error introduced by phase inconsistency. In our approach, the loss function is directly defined on the reconstructed signals, which are optimized for best separation. In addition, we train through unfolded iterations of a phase reconstruction algorithm, represented as a series of STFT and inverse STFT layers. While mask values are typically limited to lie between zero and one for approaches using the mixture phase for reconstruction, this limitation is less relevant if the estimated magnitudes are to be used together with phase reconstruction. We thus propose several novel activation functions for the output layer of the T-F masking, to allow mask values beyond one. On the publicly-available wsj0-2mix dataset, our approach achieves state-of-the-art 12.6 dB scale-invariant signal-to-distortion ratio (SI-SDR) and 13.1 dB SDR, revealing new possibilities for deep learning based phase reconstruction and representing a fundamental progress towards solving the notoriously-hard cocktail party problem. This paper considers the optimum method for locating a sync word periodically imbedded in binary data and received over the additive white Gaussian noise channel. It is shown that the optimum rule is to select the location that maximizes the sum of the correlation and a correction term. Simulations are reported that show approximately a 3-dB improvement at interesting signal-to-noise ratios compared to a pure correlation rule. Extensions are given to the "phase-shift keyed (PSK) sync" case where the detector output has a binary ambiguity and to the case of Gaussian data. Standard Mel frequency cepstrum coefficient (MFCC) computation technique utilizes discrete cosine transform (DCT) for decorrelating log energies of filter bank output. The use of DCT is reasonable here as the covariance matrix of Mel filter bank log energy (MFLE) can be compared with that of highly correlated Markov-I process. This full-band based MFCC computation technique where each of the filter bank output has contribution to all coefficients, has two main disadvantages. First, the covariance matrix of the log energies does not exactly follow Markov-I property. Second, full-band based MFCC feature gets severely degraded when speech signal is corrupted with narrow-band channel noise, though few filter bank outputs may remain unaffected. In this work, we have studied a class of linear transformation techniques based on block wise transformation of MFLE which effectively decorrelate the filter bank log energies and also capture speech information in an efficient manner. A thorough study has been carried out on the block based transformation approach by investigating a new partitioning technique that highlights associated advantages. This article also reports a novel feature extraction scheme which captures complementary information to wide band information; that otherwise remains undetected by standard MFCC and proposed block transform (BT) techniques. The proposed features are evaluated on NIST SRE databases using Gaussian mixture model-universal background model (GMM-UBM) based speaker recognition system. We have obtained significant performance improvement over baseline features for both matched and mismatched condition, also for standard and narrow-band noises. The proposed method achieves significant performance improvement in presence of narrow-band noise when clubbed with missing feature theory based score computation scheme. Abstract In a wide range of applied problems of 2D and 3D imaging a continuous formulation of the problem places great emphasis on obtaining and manipulating the Fourier transform in Polar coordinates. However, the translation of continuum ideas into practical work with data sampled on a Cartesian grid is problematic. In this article we develop a fast high accuracy Polar FFT. For a given two-dimensional signal of size N × N , the proposed algorithm's complexity is O ( N 2 log N ) , just like in a Cartesian 2D-FFT. A special feature of our approach is that it involves only 1D equispaced FFT's and 1D interpolations. A central tool in our method is the pseudo-Polar FFT, an FFT where the evaluation frequencies lie in an oversampled set of nonangularly equispaced points. We describe the concept of pseudo-Polar domain, including fast forward and inverse transforms. For those interested primarily in Polar FFT's, the pseudo-Polar FFT plays the role of a halfway point—a nearly-Polar system from which conversion to Polar coordinates uses processes relying purely on 1D FFT's and interpolation operations. We describe the conversion process, and give an error analysis of it. We compare accuracy results obtained by a Cartesian-based unequally-sampled FFT method to ours, both algorithms using a small-support interpolation and no pre-compensating, and show marked advantage to the use of the pseudo-Polar initial grid. In this paper, we have derived analytic expressions for the phase correlation of downsampled images. We have shown that for downsampled images the signal power in the phase correlation is not concentrated in a single peak, but rather in several coherent peaks mostly adjacent to each other. These coherent peaks correspond to the polyphase transform of a filtered unit impulse centered at the point of registration. The analytic results provide a closed-form solution to subpixel translation estimation, and are used for detailed error analysis. Excellent results have been obtained for subpixel translation estimation of images of different nature and across different spectral bands. The nonequispaced Fourier transform arises in a variety of application areas, from medical imaging to radio astronomy to the numerical solution of partial differential equations. In a typical problem, one is given an irregular sampling of N data in the frequency domain and one is interested in reconstructing the corresponding function in the physical domain. When the sampling is uniform, the fast Fourier transform (FFT) allows this calculation to be computed in O(N log N ) operations rather than O(N 2 ) operations. Unfortunately, when the sampling is nonuniform, the FFT does not apply. Over the last few years, a number of algorithms have been developed to overcome this limitation and are often referred to as nonuniform FFTs (NUFFTs). These rely on a mixture of interpolation and the judicious use of the FFT on an oversampled grid (A. Dutt and V. Rokhlin, SIAM J. Sci. Comput., 14 (1993), pp. 1368-1383). In this paper, we observe that one of the standard interpolation or "gridding" schemes, based on Gaussians, can be accelerated by a significant factor without precomputation and storage of the interpolation weights. This is of particular value in two- and three- dimensional settings, saving either 10 d N in storage in d dimensions or a factor of about 5-10 in CPUtime (independent of dimension). Abstract In the past years, data-driven approaches such as deep learning have been widely applied on machinery signal processing to develop intelligent fault diagnosis systems. In real-world applications, domain shift problem usually occurs where the distribution of the labeled training data, denoted as source domain, is different from that of the unlabeled testing data, known as target domain. That results in serious diagnosis performance degradation. This paper proposes a novel domain adaptation method for rolling bearing fault diagnosis based on deep learning techniques. A deep convolutional neural network is used as the main architecture. The multi-kernel maximum mean discrepancies (MMD) between the two domains in multiple layers are minimized to adapt the learned representations from supervised learning in the source domain to be applied in the target domain. The domain-invariant features can be efficiently extracted in this way, and the cross-domain testing performance can be significantly improved. Experiments on two rolling bearing datasets are carried out to validate the effectiveness of the domain adaptation approach. Comparisons with other approaches and related works demonstrate the superiority of the proposed method. The experimental results of this study suggest the proposed domain adaptation method offers a new and promising tool for intelligent fault diagnosis. The fast Fourier transform (FFT) is used widely in signal processing for efficient computation of the FT of finite-length signals over a set of uniformly spaced frequency locations. However, in many applications, one requires nonuniform sampling in the frequency domain, i.e., a nonuniform FT. Several papers have described fast approximations for the nonuniform FT based on interpolating an oversampled FFT. This paper presents an interpolation method for the nonuniform FT that is optimal in the min-max sense of minimizing the worst-case approximation error over all signals of unit norm. The proposed method easily generalizes to multidimensional signals. Numerical results show that the min-max approach provides substantially lower approximation errors than conventional interpolation methods. The min-max criterion is also useful for optimizing the parameters of interpolation kernels such as the Kaiser-Bessel function. Multimodal information processing has received considerable attention in recent years. The focus of existing research in this area has been predominantly on the use of fusion technology. In this paper, we suggest that cross-modal association can provide a new set of powerful solutions in this area. We investigate different cross-modal association methods using the linear correlation model. We also introduce a novel method for cross-modal association called Cross-modal Factor Analysis (CFA). Our earlier work on Latent Semantic Indexing (LSI) is extended for applications that use off-line supervised training. As a promising research direction and practical application of cross-modal association, cross-modal information retrieval where queries from one modality are used to search for content in another modality using low-level features is then discussed in detail. Different association methods are tested and compared using the proposed cross-modal retrieval system. All these methods achieve significant dimensionality reduction. Among them CFA gives the best retrieval performance. Finally, this paper addresses the use of cross-modal association to detect talking heads. The CFA method achieves 91.1 detection accuracy, while LSI and Canonical Correlation Analysis (CCA) achieve 66.1 and 73.9 accuracy, respectively. As shown by experiments, cross-modal association provides many useful benefits, such as robust noise resistance and effective feature selection. Compared to CCA and LSI, the proposed CFA shows several advantages in analysis performance and feature usage. Its capability in feature selection and noise resistance also makes CFA a promising tool for many multimedia analysis applications. This paper introduces an algorithm for the registration of rotated and translated volumes using the three-dimensional (3-D) pseudopolar Fourier transform, which accurately computes the Fourier transform of the registered volumes on a near-spherical 3-D domain without using interpolation. We propose a three-step procedure. The first step estimates the rotation axis. The second step computes the planar rotation relative to the rotation axis. The third step recovers the translational displacement. The rotation estimation is based on Euler's theorem, which allows one to represent a 3-D rotation as a planar rotation around a 3-D rotation axis. This axis is accurately recovered by the 3-D pseudopolar Fourier transform using radial integrations. The residual planar rotation is computed by an extension of the angular difference function to cylindrical motion. Experimental results show that the algorithm is accurate and robust to noise We show the equivalence of two state-of-the-art link prediction knowledge graph completion methods: 's holographic embedding and 's complex embedding. We first consider a spectral version of the holographic embedding, exploiting the frequency domain in the Fourier transform for efficient computation. The analysis of the resulting method reveals that it can be viewed as an instance of the complex embedding with certain constraints cast on the initial vectors upon training. Conversely, any complex embedding can be converted to an equivalent holographic embedding. Discrete Fourier transforms provide a significant speedup in the computation of convolutions in deep learning. In this work, we demonstrate that, beyond its advantages for efficient computation, the spectral domain also provides a powerful representation in which to model and train convolutional neural networks (CNNs). We employ spectral representations to introduce a number of innovations to CNN design. First, we propose spectral pooling, which performs dimensionality reduction by truncating the representation in the frequency domain. This approach preserves considerably more information per parameter than other pooling strategies and enables flexibility in the choice of pooling output dimensionality. This representation also enables a new form of stochastic regularization by randomized modification of resolution. We show that these methods achieve competitive results on classification and approximation tasks, without using any dropout or max-pooling. Finally, we demonstrate the effectiveness of complex-coefficient spectral parameterization of convolutional filters. While this leaves the underlying model unchanged, it results in a representation that greatly facilitates optimization. We observe on a variety of popular CNN configurations that this leads to significantly faster convergence during training. Discrete Fourier transforms provide a significant speedup in the computation of convolutions in deep learning. In this work, we demonstrate that, beyond its advantages for efficient computation, the spectral domain also provides a powerful representation in which to model and train convolutional neural networks (CNNs). We employ spectral representations to introduce a number of innovations to CNN design. First, we propose spectral pooling, which performs dimensionality reduction by truncating the representation in the frequency domain. This approach preserves considerably more information per parameter than other pooling strategies and enables flexibility in the choice of pooling output dimensionality. This representation also enables a new form of stochastic regularization by randomized modification of resolution. We show that these methods achieve competitive results on classification and approximation tasks, without using any dropout or max-pooling. Finally, we demonstrate the effectiveness of complex-coefficient spectral parameterization of convolutional filters. While this leaves the underlying model unchanged, it results in a representation that greatly facilitates optimization. We observe on a variety of popular CNN configurations that this leads to significantly faster convergence during training. We explore efficient domain adaptation for the task of statistical machine translation based on extracting sentences from a large general-domain parallel corpus that are most relevant to the target domain. These sentences may be selected with simple cross-entropy based methods, of which we present three. As these sentences are not themselves identical to the in-domain data, we call them pseudo in-domain subcorpora. These subcorpora -- 1 the size of the original -- can then used to train small domain-adapted Statistical Machine Translation (SMT) systems which outperform systems trained on the entire corpus. Performance is further improved when we use these domain-adapted models in combination with a true in-domain model. The results show that more training data is not always better, and that best results are attained via proper domain-relevant data selection, as well as combining in- and general-domain systems during decoding. Efficient similarity retrieval from large-scale multimodal database is pervasive in current search systems with the big data tidal wave. To support queries across content modalities, the system should enable cross-modal correlation and computation-efficient indexing. While hashing methods have shown great potential in approaching this goal, current attempts generally failed to learn isomorphic hash codes in a seamless scheme, that is, they embed multiple modalities into a continuous isomorphic space and then threshold embeddings into binary codes, which incurred substantial loss of search quality. In this paper, we establish seamless multimodal hashing by proposing a novel Compositional Correlation Quantization (CCQ) model. Specifically, CCQ jointly finds correlation-maximal mappings that transform different modalities into an isomorphic latent space, and learns compositional quantizers that quantize the isomorphic latent features into compact binary codes. An optimization framework is developed to preserve both intra-modal similarity and inter-modal correlation while minimizing both reconstruction and quantization errors, which can be trained from both paired and unpaired data in linear time. A comprehensive set of experiments clearly show the superior effectiveness and efficiency of CCQ against the state-of-the-art techniques on both unimodal and cross-modal search tasks. We propose an indexing method for time sequences for processing similarity queries. We use the Discrete Fourier Transform (DFT) to map time sequences to the frequency domain, the crucial observation being that, for most sequences of practical interest, only the first few frequencies are strong. Another important observation is Parseval's theorem, which specifies that the Fourier transform preserves the Euclidean distance in the time or frequency domain. Having thus mapped sequences to a lower-dimensionality space by using only the first few Fourier coefficients, we use R * -trees to index the sequences and efficiently answer similarity queries. We provide experimental results which show that our method is superior to search based on sequential scanning. Our experiments show that a few coefficients (1–3) are adequate to provide good performance. The performance gain of our method increases with the number and length of sequences.