We introduce NeRD, a new demosaicking method for generating full-color images from Bayer patterns. Our approach leverages advancements in neural fields to perform demosaicking by representing an image as a coordinate-based neural network with sine activation functions. The inputs to the network are spatial coordinates and a low-resolution Bayer pattern, while the outputs are the corresponding RGB values. An encoder network, which is a blend of ResNet and U-net, enhances the implicit neural representation of the image to improve its quality and ensure spatial consistency through prior learning. Our experimental results demonstrate that NeRD outperforms traditional and state-of-the-art CNN-based methods and significantly closes the gap to transformer-based methods.

This paper proposes a novel approach to real-time automatic rim detection, classification, and inspection by combining traditional computer vision and deep learning techniques. At the end of every automotive assembly line, a quality control process is carried out to identify any potential defects in the produced cars. Common yet hazardous defects are related, for example, to incorrectly mounted rims. Routine inspections are mostly conducted by human workers that are negatively affected by factors such as fatigue or distraction. We have designed a new prototype to validate whether all four wheels on a single car match in size and type. Additionally, we present three comprehensive open-source databases, CWD1500, WHEEL22, and RB600, for wheel, rim, and bolt detection, as well as rim classification, which are free-to-use for scientific purposes.

Abstract Blur is an image degradation that makes object recognition challenging. Restoration approaches solve this problem via image deblurring, deep learning methods rely on the augmentation of training sets. Invariants with respect to blur offer an alternative way of describing and recognising blurred images without any deblurring and data augmentation. In this paper, we present an original theory of blur invariants. Unlike all previous attempts, the new theory requires no prior knowledge of the blur type. The invariants are constructed in the Fourier domain by means of orthogonal projection operators and moment expansion is used for efficient and stable computation. Applying a general substitution rule, combined invariants to blur and spatial transformations are easy to construct and use. Experimental comparison to Convolutional Neural Networks shows the advantages of the proposed theory.

Vector fields are a special kind of multidimensional data, which are in a certain sense similar to digital color images, but are distinct from them in several aspects. In each pixel, the field is assigned to a vector that shows the direction and the magnitude of the quantity, which has been measured. To detect the patterns of interest in the field, special matching methods must be developed. In this paper, we propose a method for the description and matching of vector field patterns under an unknown affine transformation of the field. Unlike digital images, transformations of vector fields act not only on the spatial coordinates but also on the field values, which makes the detection different from the image case. To measure the similarity between the template and the field patch, we propose original invariants with respect to total affine transformation. They are designed from the vector field moments. It is demonstrated by experiments on real data from fluid mechanics that they perform significantly better than potential competitors.

This article is a comment on the recent TPAMI paper (Gopalan et al., 2012) that introduced a blur-invariant distance measure between two images. We point out two mistakes of the theory presented in (Gopalan et al., 2012) and propose a correction. We also compare the original and corrected methods experimentally.

In this paper, a new recursive structure based on the convolution model of discrete cosine transform (DCT) for designing of a finite impulse response (FIR) digital filter is proposed. In our derivation, we start with the convolution model of DCT-II to use its Z-transform for the proposed filter structure perspective. Moreover, using the same algorithm, a filter base implementation of the inverse DCT (IDCT) for image reconstruction is developed. The computational time experiments of the proposed DCT/IDCT filter(s) demonstrate that the proposed filters achieve faster elapsed CPU time compared to the others. The image filtering and reconstruction performance of the proposed approach on ultrasound images are presented to validate the theoretical framework.

The paper presents a new theory of combined moment invariants to Gaussian blur and spatial affine transformation. The blur kernel may be arbitrary oriented, scaled and elongated. No prior information about the kernel parameters and about the underlaying affine transform is required. The main idea, expressed by the Substitution Theorem, is to substitute pure blur invariants into traditional affine moment invariants. Potential applications of the new descriptors are in blur-invariant image recognition and in robust template matching.

Vector field (VF) is a special kind of multidimensional data. In each pixel, VF contains information about the direction and the magnitude of the measured quantity. To detect the patterns of interest in the field, special matching methods must be developed. We propose a method for the description and matching of VF patterns under an unknown affine transformation of the field. Unlike digital images, transformations of VFs act not only on the spatial coordinates but also on the field values, which makes the detection different. To measure the similarity between the template and the field patch, we propose original invariants with respect to affine transformation designed from moments. Their performance is demonstrated by experiments on real data from fluid mechanics.

We propose a method for the recognition of vector field patterns under an unknown rotation. The rotation is modeled as a total transformation, which is applied on both spatial coordinates and field values. The invariants are constructed from orthogonal Gaussian-Hermite moments. Their numerical stability and recognition power are shown to be better than those of the invariants published so far.

In this paper, we propose a new theory of invariants to Gaussian blur. We introduce a notion of a primordial image as a canonical form of all Gaussian blur-equivalent images. The primordial image is defined in spectral domain by means of projection operators. We prove that the moments of the primordial image are invariant to Gaussian blur and we derive recursive formulas for their direct computation without actually constructing the primordial image itself. We show how to extend their invariance also to image rotation. The application of these invariants is in blur-invariant image comparison and recognition. In the experimental part, we perform an exhaustive comparison with two main competitors: 1) the Zhang distance and 2) the local phase quantization.

Videokymography (VKG) is a high-speed medical imaging technique used in laryngology and phoniatrics for examination of vocal fold vibrations, it offers important characteristics for diagnosis and treatment of voice disorders. VKG repeatedly scans only a single line from the scene and captures movements of vocal folds in this region of interest. This paper proposes methods for computer assisted evaluation of diagnostically important vibration features, related to movements of vocal folds and their surroundings. They are derived from existing as well as newly developed methods of digital image processing, mainly based on data segmentation and morphological operations. Performance of the developed methods is compared to expert manual assessments and it proves to be comparable with clinicians conclusions.

In this paper we introduce a new theory of blur invariants. Blur invariants are image features which preserve their values if the image is convolved by a point-spread function (PSF) of a certain class. We present the invariants to convolution with an arbitrary N-fold symmetric PSF, both in Fourier and image domain. We introduce a notion of a primordial image as a canonical form of all blur-equivalent images. It is defined in spectral domain by means of projection operators. We prove that the moments of the primordial image are invariant to blur and we derive recursive formulae for their direct computation without actually constructing the primordial image. We further prove they form a complete set of invariants and show how to extent their invariance also to translation, rotation and scaling. We illustrate by simulated and real-data experiments their invariance and recognition power. Potential applications of this method are wherever one wants to recognize objects on blurred images.

In this letter, we propose a global method for registering color images with respect to translation. Our approach is based on the idea of representing translations as convolutions with unknown shifted delta functions, and performing Wiener deconvolution in order to recover the shift between two images. We then derive a quaternionic version of the Wiener deconvolution filter in order to register color images. The use of Wiener filter also allows us to explicitly take into account the effect of noise. We prove that the well-known algorithm of phase correlation is a special case of our method, and we experimentally demonstrate the advantages of our approach by comparing it to other known generalizations of the phase correlation algorithm.

In this paper, we extend our recent registration method designed specifically for registering blurred images. The original method works for unknown blurs, assuming the blurring point-spread function (PSF) exhibits an N -fold rotational symmetry. Here, we also generalize the theory to the case of dihedrally symmetric blurs, which are produced by the PSFs having both rotational and axial symmetries. Such kind of blurs are often found in unfocused images acquired by digital cameras, as in out-of-focus shots the PSF typically mimics the shape of the shutter aperture. This makes our registration algorithm particularly well-suited in applications where blurred image registration must be used as a preprocess step of an image fusion algorithm, and where common registration methods fail, due to the amount of blur. We demonstrate that the proposed method leads to an improvement of the registration performance, and we show its applicability to real images by providing successful examples of blurred image registration followed by depth-of-field extension and multichannel blind deconvolution.

We present a content-based image retrieval method which is particularly designed for noisy images. The images are retrieved according to histogram similarity. To reach high robustness to noise, the histograms are described by novel features which are insensitive to convolution with a Gaussian kernel, i.e. insensitive to a Gaussian additive noise in original images. The advantage of the new method is demonstrated experimentally on real data.

We propose a method for removal of space-variant blur from images predominantly degraded by camera shake without any knowledge of camera trajectory. Blurs are first estimated in a small number of image patches. We derive a novel parametric blur interpolation method and discuss conditions under which it can be used to exactly calculate blurs for every pixel position. Having this information, we restore the sharp image by a standard regularization technique. Performance of the proposed method is experimentally validated.

Steerability is a useful and important property of "kernel" functions. It enables certain complicated operations involving orientation manipulation on images to be executed with high efficiency. Thus, we focus our attention on the steerability of Hermite polynomials and their versions modulated by the Gaussian function with different powers, defined as the Hermite kernel. Certain special cases of such kernel, Hermite polynomials, Hermite functions and Gaussian derivatives are discussed in detail. Correspondingly, these cases demonstrate that the Hermite kernel is a powerful and effective tool for image processing. Furthermore, the steerability of the Hermite kernel is proved with the help of a property of Hermite polynomials revealing the rule concerning the product of two Hermite polynomials after coordination rotation. Consequently, any order of the Hermite kernel inherits steerability. Moreover, a couple sets of an explicit interpolation function and basis function can be directly obtained. We provide some examples to verify steerability of the Hermite kernel. Experimental results show the effectiveness of steerability and its potential applications in the fields of image processing and computer vision.

In this paper, we propose a new registration method designed particularly for registering differently blurred images. Such a task cannot be successfully resolved by traditional approaches. Our method is inspired by traditional phase correlation, which is now applied to certain blur-invariant descriptors instead of the original images. This method works for unknown blurs assuming the blurring PSF exhibits an N-fold rotational symmetry. It does not require any landmarks. We have experimentally proven its good performance, which is not dependent on the amount of blur. In this paper, we explicitly address only registration with respect to translation, but the method can be readily generalized to rotation and scaling.

This paper deals with moment invariants with respect to image blurring. It is mainly a reaction to the works of Zhang and Chen , recently published in these Transactions. We present a general method on how to construct blur invariants from arbitrary moments and show that it is no longer necessary to separately derive the invariants for each polynomial basis. We show how to discard dependent terms in blur invariants definition and discuss a proper implementation of the invariants in orthogonal bases using recurrent relations. An example for Legendre moments is given.

A new method of moment computation based on decomposition of the object into rectangular blocks is presented. The decomposition is accomplished by means of distance transform. The method is compared with earlier morphological methods, namely with erosion decomposition to squares. All the methods are also compared with direct computation by definition.

In many real applications, traditional super-resolution (SR) methods fail to provide high-resolution images due to objectionable blur and inaccurate registration of input low-resolution images. Only integer resolution enhancement factors, such as 2 or 3, are often considered, but non-integer factors between 1 and 2 are also important in real cases. We introduce a method to SR and deconvolution, which assumes no prior information about the shape of degradation blurs, incorporates registration parameters, and is properly defined for any rational (fractional) resolution factor. The method minimizes a regularized energy function with respect to the high-resolution image and blurs, where regularization is carried out in both the image and blur domains. The blur regularization is based on a generalized multi-channel blind deconvolution constraint derived in the paper. An extension to color images is briefly discussed. Experiments on real data illustrate robustness to noise and other advantages of the method.

In many real applications traditional superresolution methods fail to provide high-resolution images due to objectionable blur and inaccurate registration of input low-resolution images. In this paper, we present a method of superresolution and blind deconvolution of video sequences and address problems of misregistration, local motion and change of illumination. The method processes the video by applying temporal windows, masking out regions of misregistration, and minimizing a regularized energy function with respect to the high-resolution frame and blurs, where regularization is carried out in both the image and blur domains. Experiments on real video sequences illustrate robustness of the method.

Pattern recognition of objects on affinely distorted images based on moments is important task researched for many years. Affinemoment invariants are significant tool for it. They can be generated by a few methods. Automated direct solution of the Cayley - Aronhold differential equation has not been referred yet. It makes possible to generate invariants with much higher weights than other methods, but we must pay more attention to the numerical stability of the computation. The method is demonstrated on examples.

We examine the problem of restoration from multiple images degraded by camera motion blur. We consider scenes with significant depth variations resulting in space-variant blur. The proposed algorithm can be applied if the camera moves along an arbitrary curve parallel to the image plane, without any rotations. The knowledge of camera trajectory and camera parameters is not necessary. At the input, the user selects a region where depth variations are negligible. The algorithm belongs to the group of variational methods that estimate simultaneously a sharp image and a depth map, based on the minimization of a cost functional. To initialize the minimization, it uses an auxiliary window-based depth estimation algorithm. Feasibility of the algorithm is demonstrated by three experiments with real images.

This paper presents a new approach to the blind deconvolution and superresolution problem of multiple degraded low-resolution frames of the original scene. We do not assume any prior information about the shape of degradation blurs. The proposed approach consists of building a regularized energy function and minimizing it with respect to the original image and blurs, where regularization is carried out in both the image and blur domains. The image regularization based on variational principles maintains stable performance under severe noise corruption. The blur regularization guarantees consistency of the solution by exploiting differences among the acquired low-resolution images. Several experiments on synthetic and real data illustrate the robustness and utilization of the proposed technique in real applications.

In this paper, a new set of moment invariants with respect to rotation, translation, and scaling suitable for recognition of objects having N-fold rotation symmetry are presented. Moment invariants described earlier cannot be used for this purpose because most moments of symmetric objects vanish. The invariants proposed here are based on complex moments. Their independence and completeness are proven theoretically and their performance is demonstrated by experiments.

Materials research of microscopic cross-sections of paintings color layers is a very useful tool. It gives the restorers better insight into the technique, reveals how the artwork was created and what kind of materials was used. The proposed approach solves the problem of the proper spatial alignment of visible light and ultraviolet light images of cross-sections for further analysis by means of multimodal geometrical image registration. Then, the application offers primary segmentation of color layers. Second part of our work deals with automatic image retrieval, as a part of designing a database of laboratory research reports for restoration purposes. The aim is to facilitate search for reports about artworks with similar characteristic, based on the cross-section images.

Existing multichannel blind restoration techniques assume perfect spatial alignment of channels, correct estimation of blur size, and are prone to noise. We developed an alternating minimization scheme based on a maximum a posteriori estimation with a priori distribution of blurs derived from the multichannel framework and a priori distribution of original images defined by the variational integral. This stochastic approach enables us to recover the blurs and the original image from channels severely corrupted by noise. We observe that the exact knowledge of the blur size is not necessary, and we prove that translation misregistration up to a certain extent can be automatically removed in the restoration process.

The paper is devoted to the moment invariants with respect to projective transform. It has been a common belief that such invariants do not exist. We show that projective moment invariants exist in a form of infinite series containing moments with positive as well as negative indices.

We present the construction of combined blur and rotation moment invariants in arbitrary number of dimensions. Moment invariants to convolution with an arbitrary centrosymmetric filter are derived first, and then their rotationally invariant forms are found by means of group representation theory to achieve the desired combined invariance. Several examples of the invariants are calculated explicitly to illustrate the proposed procedure. Their invariance, robustness, and capability of using in template matching and in image registration are demonstrated on 3D MRI data and 2D indoor images.

Blind image deconvolution is required in many applications of microscopy imaging, remote sensing, and astronomical imaging. Unfortunately in a single-channel framework, serious conceptual and numerical problems are often encountered. Very recently, an eigenvector-based method (EVAM) was proposed for a multichannel framework which determines perfectly convolution masks in a noise-free environment if channel disparity, called co-primeness, is satisfied. We propose a novel iterative algorithm based on recent anisotropic denoising techniques of total variation and a Mumford-Shah functional with the EVAM restoration condition included. A linearization scheme of half-quadratic regularization together with a cell-centered finite difference discretization scheme is used in the algorithm and provides a unified approach to the solution of total variation or Mumford-Shah. The algorithm performs well even on very noisy images and does not require an exact estimation of mask orders. We demonstrate capabilities of the algorithm on synthetic data. Finally, the algorithm is applied to defocused images taken with a digital camera and to data from astronomical ground-based observations of the Sun.

The topic of the paper is to estimate parameters of the camera motion using images taken at initial and current positions of the camera. An original method handling defocused images or images blurred in other ways is proposed. The method is based on registering the images by means of detected control points (CP) and so-called combined invariants. These features are invariant both to rigid-body transform and to blurring caused by convolution with an arbitrary centrosymmetric point-spread function (PSF). Thanks to this, the camera position can be estimated directly from defocused images without any deblurring.

We present an application of digital image processing to the analysis of the conservation of a medieval mosaic. The art piece is the "The Last Judgement" mosaic, situated on the wall of St Vitus Cathedral in Prague, Czech Republic. A 19/sup th/ century historical photograph of the mosaic was compared with a photograph of its current reconstructed state. The images were first preprocessed to increase their quality (noise reduction, deblurring). In the second stage, geometrical differences between images were removed by means of image registration techniques. Finally, differences between the current and historical photographs were identified.

In this correspondence, we prove that the affine invariants, for image registration and object recognition, proposed recently by Yang and Cohen (see ibid., vol.8, no.7, p.934-46, July 1999) are algebraically dependent. We show how to select an independent and complete set of the invariants. The use of this new set leads to a significant reduction of the computing complexity without decreasing the discrimination power.

We present a multichannel blind deconvolution method based on so-called subspace technique that was originally proposed by Harikumar and Bresler (1996, 1999). When at least two differently degraded images (channels) of the original scene are provided, the method is better conditioned than classical single channel ones. In comparison with earlier multichannel blind deconvolution techniques the subspace method is not iterative and this possibly implies an implementation that can be computationally more efficient. An application of the proposed method to the restoration of the images of sunspots is presented.

This paper deals with effective calculation of moments of binary images. Recently, Spiliotis and Mertzios (see ibid., vol.7, p.1609-15, Nov. 1998) published a method based on image block representation (IBR). We propose a refinement of their method which yields exact results and performs even more effectively.

A new class of moment-based features invariant to image rotation, translation, scaling, contrast changes and also to convolution with an unknown PSF are introduced in this paper. These features can be used for the recognition of objects captured by a nonideal imaging system of unknown position and blurring parameters.

A new method of multichannel blind deconvolution is introduced. The algorithm is simple, computationally efficient and does not need any statistical presumptions about the image. Any a priori knowledge about the PSF and the original can be incorporated very easily. Numerical simulations and experiments give promising results comparing to other restoration methods.

Analysis and interpretation of an image which was acquired by a nonideal imaging system is the key problem in many application areas. The observed image is usually corrupted by blurring, spatial degradations, and random noise. Classical methods like blind deconvolution try to estimate the blur parameters and to restore the image. We propose an alternative approach. We derive the features for image representation which are invariant with respect to blur regardless of the degradation PSF provided that it is centrally symmetric. As we prove in the paper, there exist two classes of such features: the first one in the spatial domain and the second one in the frequency domain. We also derive so-called combined invariants, which are invariant to composite geometric and blur degradations. Knowing these features, we can recognize objects in the degraded scene without any restoration.

The paper is devoted to the feature-based recognition of degraded signals acquired by a linear time-invariant system The proposed approach consists of describing signals by features which are invariant with respect to the degradation and recognizing signals in the feature space. Neither impulse response identification nor signal restoration are required. Thanks to this, the new approach is in many applications much more effective than the classical one based on blind deconvolution. Two sets of appropriate blur-invariant features (the first one in time domain, the other one in spectral domain) are introduced in this paper. The proof of their invariance is given and their performance is illustrated by numerical experiments.

The article is devoted to the feature-based recognition of blurred images acquired by a linear shift-invariant imaging system against an image database. The proposed approach consists of describing images by features that are invariant with respect to blur and recognizing images in the feature space. The PSF identification and image restoration are not required. A set of symmetric blur invariants based on image moments is introduced. A numerical experiment is presented to illustrate the utilization of the invariants for blurred image recognition. Robustness of the features is also briefly discussed.

The paper deals with features of a point set which are invariant with respect to the projective transform. First, some properties of the area of a triangle under a projective transform and the cross-ratio are discussed. Two types of projective triangular invariants of point sets are derived. One of them is a quotient of two different products of the areas of triangles formed by the vertices of the polygon. It is invariant to the labeling of the vertices. The number of the features is discussed and a method for its reduction is presented. The other type of features is expressed as functions of a five-point cross-ratios and it is invariant to the choice of labeling of the points. The possibility of the normalization of these invariants is shown. The performance of the features is demonstrated by numerical experiments.

A new method is described for automatic control point selection and matching. First, reference and sensed images are segmented and closed-boundary regions are extracted. Each region is represented by a set of affine-invariant moment-based features. Correspondence between the regions is then established by a two-stage matching algorithm that works both in the feature space and in the image space. Centers of gravity of corresponding regions are used as control points. A practical use of the proposed method is demonstrated by registration of SPOT and Landsat TM images. It is shown that the authors' method can produce subpixel registration accuracy.>

A model of finite Radon transforms composed of Radon projections is presented. The model generalizes to finite group projections in the classical Radon transform theory. The Radon projector averages a function on a group over cosets of a subgroup. Reconstruction formulae that were formally similar to the convolved backprojection ones are derived, and an iterative reconstruction technique is found to converge after a finite number of steps. Applying these results to the group Z/sub 2//sup P/, new computationally favorable image representations have been obtained. A numerical study of the transform coding aspects is attached.>