Gaussian Scale Space Research Articles

S-AKAZE: An effective point-based method for image matching

This paper presents a new point-based matching method, which integrates A-KAZE feature with improved SIFT descriptor. In previous studies, all the SIFT-based algorithms use the Gaussian scale space and Gaussian derivatives as smoothing kernel, but the Gaussian blurring does not self-adapt to the natural boundaries of objects and smoothes details and noise to the same extent at all scale levels, which will reduce localization accuracy and distinctiveness. Unlike SIFT feature, A-KAZE feature is built on nonlinear scale space by using Fast Explicit Diffusion (FED) schemes, which can blur the noise and remain the details or edges at the same time. Therefore we replace SIFT with A-KAZE to conduct feature detection. Then, in order to solve the problem that the combination of A-KAZE feature and SIFT descriptor is not rotation invariant, we use a SURF-like method to calculate the dominant orientations of keypoints and hereafter our method is thus named as S-AKAZE. Experiments on Mikolajczyk and Schmid dataset prove the high accuracy of our proposed method and experiments on four different types of remote sensing image pairs demonstrate an outstanding performance in remote sensing image matching.

Hierarchical Gaussian Scale-Space on Androgenic Hair Pattern Recognition

Androgenic hair pattern stated to be the new biometric trait since 2014. The research to improve the performance of androgenic hair pattern recognition system has begun to be developed due to the problems that occurred when other apparent biometric trait such as face is hidden from sight. The recognition system was built with hierarchical Gaussian scale-space using 4 octaves and 3 levels in each octave. The system also implemented the equalization process to adjust image’s intensity by using histogram equalization. We analyzed 400 images of androgenic hair in the database that were analyzed using 2-fold and 10-fold cross validation and Euclidean distance to classify it. The experimental results showed that our proposed method gave better performance compared to previous work that used Haar wavelet transformation and principal component analysis as the main method. The best recognition precision was 94.23 % obtained from the base octave with the third level using histogram equalization and 10-fold cross validation.

Computing an Exact Gaussian Scale-Space

Gaussian convolution is one of the most important algorithms in image processing. The present work focuses on the computation of the Gaussian scale-space, a family of increasingly blurred images, responsible, among other things, for the scale-invariance of SIFT, a popular image matching algorithm. We discuss and numerically analyze the precision of three different alternatives for defining a discrete counterpart to the continuous Gaussian smoothing operator. This study is focused on low blur levels, that are crucial for the scale-space accuracy. Source Code An ANSI C source code implementation of the described algorithms is accessible at the IPOL web page of this article 1 , together with an on-line demo.

Appell sequences, continuous wavelet transforms and series expansions

A series expansion with remainder for functions in a Sobolev space is derived in terms of the classical Bernoulli polynomials, the B -spline scale-space and the continuous wavelet transforms with the derivatives of the standardized B -splines as mother wavelets. In the limit as their orders tend to infinity, the B -splines and their derivatives converge to the Gaussian function and its derivatives respectively, the associated Bernoulli polynomials converge to the Hermite polynomials, and the corresponding series expansion is an expansion in terms of the Hermite polynomials, the Gaussian scale-space and the continuous wavelet transforms with the derivatives of the Gaussian function as mother wavelets. A similar expansion is also derived in terms of continuous wavelet transforms in which the mother wavelets are the spline framelets that approximate the derivatives of the standardized B -splines.

Generalised morphological image diffusion

Relationships between linear and morphological scale-spaces have been considered by various previous works. The aim of this paper is to study how to generalise the discrete and continuous diffusion-based approaches in order to introduce nonlinear filters whose limit effects mimic the asymmetric behaviour of morphological dilation and erosion, as well as other multiscale filters, hybrid between the standard linear and morphological filters. A methodology based on the counter-harmonic mean is adopted here. Partial differential equations are formulated and details of numerical implementation are discussed to illustrate the various studied cases: isotropic, edge-preserving and coherence-enhancing diffusion. We also found a new way to derive the classical link between Gaussian scale-space and dilation/erosion scale-spaces based on quadratic structuring functions in the discrete and continuous setting. We have included some preliminary applications of the generalised morphological diffusion to solve image processing problems such as denoising and image enhancement in the case of asymmetric bright/dark image properties.

HEp-2 cell classification: The role of Gaussian Scale Space Theory as a pre-processing approach

Indirect Immunofluorescence Imaging of Human Epithelial Type 2 (HEp-2) cells is an effective way to identify the presence of Anti-Nuclear Antibody (ANA). Most existing works on HEp-2 cell classification mainly focus on feature extraction, feature encoding and classifier design. Very few efforts have been devoted to study the importance of the pre-processing techniques. In this paper, we analyze the importance of the pre-processing, and investigate the role of Gaussian Scale Space (GSS) theory as a pre-processing approach for the HEp-2 cell classification task. We validate the GSS pre-processing under the Local Binary Pattern (LBP) and the Bag-of-Words (BoW) frameworks. Under the BoW framework, the introduced pre-processing approach, using only one Local Orientation Adaptive Descriptor (LOAD), achieved superior performance on the Executable Thematic on Pattern Recognition Techniques for Indirect Immunofluorescence (ET-PRT-IIF) image analysis. Our system, using only one feature, outperformed the winner of the ICPR 2014 contest that combined four types of features. Meanwhile, the proposed pre-processing method is not restricted to this work; it can be generalized to many existing works.

Shape recognition using orientational and morphological scale‐spaces of curvatures

In this study, a scale‐invariant representation for closed planar curves (silhouettes) is proposed. The orientations of all points within the Gaussian scale‐space of the curve are extracted. This orientation scale‐space is used to create the silhouette orientation image in which the positions of each pixel indicate the curve's pixel positions and scales, whereas the colour represents orientation. The representation is extracted for multiple levels of the morphological scale‐space of the silhouette. The proposed representation is invariant to scale and transformable under planar rotation. Using linear and non‐linear distance learning methods, experiments on the MPEG7, ETH80 and Kimia shape datasets were conducted, with results indicating an advanced recognition capability.

Multispectral Image Alignment With Nonlinear Scale-Invariant Keypoint and Enhanced Local Feature Matrix

The scale space-based method has been recently studied for multispectral alignment; however, due to the significant intensity difference between the image pairs, there are usually not enough keypoint correspondences found, and the robustness of the alignment tends to be compromised. In this letter, we attempt to improve the performance from the following two aspects: 1) to avoid the boundary blurring of Gaussian scale space, we adopt nonlinear scale space to explore more keypoints with potential of being correctly matched, and 2) a robust feature descriptor is proposed, and the resulting feature matrix is matched using the previously proposed rotation-invariant distance to obtain more correct keypoint correspondences. Experimental results for multispectral remote images indicate that the proposed method improves the matching performance compared to state-of-the-art methods in terms of correctly matched number of keypoints, aligning accuracy, and rate of correctly matched image pairs. It is also revealed in this letter that, if the descriptor is carefully designed, the local features are distinctive enough for produce good matching even when the main orientation is not present.

Human visual system consistent quality assessment for remote sensing image fusion

Quality assessment for image fusion is essential for remote sensing application. Generally used indices require a high spatial resolution multispectral (MS) image for reference, which is not always readily available. Meanwhile, the fusion quality assessments using these indices may not be consistent with the Human Visual System (HVS). As an attempt to overcome this requirement and inconsistency, this paper proposes an HVS-consistent image fusion quality assessment index at the highest resolution without a reference MS image using Gaussian Scale Space (GSS) technology that could simulate the HVS. The spatial details and spectral information of original and fused images are first separated in GSS, and the qualities are evaluated using the proposed spatial and spectral quality index respectively. The overall quality is determined without a reference MS image by a combination of the proposed two indices. Experimental results on various remote sensing images indicate that the proposed index is more consistent with HVS evaluation compared with other widely used indices that may or may not require reference images.

Rotation and scale invariant shape context registration for remote sensing images with background variations

Multitemporal remote sensing images generally suffer from background variations, which significantly disrupt traditional region feature and descriptor abstracts, especially between pre and postdisasters, making registration by local features unreliable. Because shapes hold relatively stable information, a rotation and scale invariant shape context based on multiscale edge features is proposed. A multiscale morphological operator is adapted to detect edges of shapes, and an equivalent difference of Gaussian scale space is built to detect local scale invariant feature points along the detected edges. Then, a rotation invariant shape context with improved distance discrimination serves as a feature descriptor. For a distance shape context, a self-adaptive threshold (SAT) distance division coordinate system is proposed, which improves the discriminative property of the feature descriptor in mid-long pixel distances from the central point while maintaining it in shorter ones. To achieve rotation invariance, the magnitude of Fourier transform in one-dimension is applied to calculate angle shape context. Finally, the residual error is evaluated after obtaining thin-plate spline transformation between reference and sensed images. Experimental results demonstrate the robustness, efficiency, and accuracy of this automatic algorithm.

Copy-move forgery detection based on scaled ORB

To solve the problem of the false matching and low robustness in detecting copy-move forgeries, a new method was proposed in this study. It involves the following steps: first, establish a Gaussian scale space; second, extract the orientated FAST key points and the ORB features in each scale space; thirdly, revert the coordinates of the orientated FAST key points to the original image and match the ORB features between every two different key points using the hamming distance; finally, remove the false matched key points using the RANSAC algorithm and then detect the resulting copy-move regions. The experimental results indicate that the new algorithm is effective for geometric transformation, such as scaling and rotation, and exhibits high robustness even when an image is distorted by Gaussian blur, Gaussian white noise and JPEG recompression; the new algorithm even has great detection on the type of hiding object forgery.

结合Harris与SIFT算子的图像快速配准算法

A new method for fast image registration based on improved Harris-Sift algorithm is proposed. Firstly,classic Harris algorithm is improved by building Gaussian scale space to extract scale invariant Harris corners and they are refined to sub-pixel corners using Forsnter algorithm. Then the SIFT descriptor is utilized to characterize those feature points and the matching procedure is carried out via randomized kd trees. At last,RANSAC is used to remove wrong matches and the optimal transform parameters are estimated using the least square method to accomplish the image registration process. The experimental results demonstrate that compared with the classic SIFT algorithm the proposed method decreases the cost time of the registration procedure mostly by 64% while almost keeping the same performance.

Anatomy of the SIFT Method

This dissertation contributes to an in-depth analysis of the SIFT method. SIFT is the most popular and the first efficient image comparison model. SIFT is also the first method to propose a practical scale-space sampling and to put in practice the theoretical scale invariance in scale space. It associates with each image a list of scale invariant (also rotation and translation invariant) features which can be used for comparison with other images. Because after SIFT feature detectors have been used in countless image processing applications, and because of an intimidating number of variants, studying an algorithm that was published more than a decade ago may be surprising. It seems however that not much has been done to really understand this central algorithm and to find out exactly what improvements we can hope for on the matter of reliable image matching methods. Our analysis of the SIFT algorithm is organized as follows. We focus first on the exact computation of the Gaussian scale-space which is at the heart of SIFT as well as most of its competitors. We provide a meticulous dissection of the complex chain of transformations that form the SIFT method and a presentation of every design parameter from the extraction of invariant keypoints to the computation of feature vectors. Using this documented implementation permitting to vary all of its own parameters, we define a rigorous simulation framework to find out if the scale-space features are indeed correctly detected by SIFT, and which sampling parameters influence the stability of extracted keypoints. This analysis is extended to see the influence of other crucial perturbations, such as errors on the amount of blur, aliasing and noise. This analysis demonstrates that, despite the fact that numerous methods claim to outperform the SIFT method, there is in fact limited room for improvement in methods that extract keypoints from a scale-space. The comparison of many detectors proposed in SIFT competitors is the subject of the last part of this thesis. The performance analysis of local feature detectors has been mainly based on the repeatability criterion. We show that this popular criterion is biased toward methods producing redundant (overlapping) descriptors. We therefore propose an amended evaluation metric and use it to revisit a classic benchmark. For the amended repeatability criterion, SIFT is shown to outperform most of its more recent competitors. This last fact corroborates the unabating interest in SIFT and the necessity of a thorough scrutiny of this method.

Two-view line matching algorithm based on context and appearance in low-textured images

A novel approach for line detection and matching is proposed, aimed at achieving good performance with low-textured scenes, under uncontrolled illumination conditions. Line detection is performed by means of phase-based edge detector over Gaussian scale-space, followed by a multi-scale fusion stage which has been proven to be profitable in minimizing the number of fragmented and overlapped segments. Line matching is performed by an iterative process that uses structural information collected through the use of different line neighborhoods, making the set of matched lines grow robustly at each iteration. Results show that this approach is suitable to deal with low-textured scenes, and also robust under a wide variety of image transformations.

No-Reference Image Quality Assessment through SIFT Intensity

SIFT (Scale Invariant Feature Transform) points are scale-space extreme points, representing local minutiae structure features in the Gaussian scale space. SIFT intensity, as a novel no-ref erence metric, is feasible to assess various common distortions without the access to reference images. The metric introduces image preprocessing: neighborhood enhancement through contrast enhancement of adjacent pixels to reduce false SIFT points triggered by random signals; double-size image magnification through linear interpolation to amplify distortion effects to improve its sensitivity to image q uality. SIFT intensity is defined as the number of SIFT points in a unit region and is calculated based on the first octave of the difference-of-Gaussian scale space. Experimental results demonstrate that SIFT intensity is superior to existing classic no-referenc e metrics and can be used to assess different distortions.

Notes on Discrete Gaussian Scale Space

Gaussian scale space is a well-known linear multi-scale representation for continuous signals. The exploration of its so-called deep structure by tracing critical points over scale has various theoretical applications and allows for the construction of a scale space hierarchy tree. However, implementation issues arise, caused by discretization and quantization errors. In order to develop more robust scale space based algorithms, the discrete nature of computer processed signals has to be taken into account. We propose suitable neighborhoods, boundary conditions, and sampling methods. In analogy to prevalent approaches and inspired by Lindeberg's scale space primal sketch, a discretized diffusion equation is derived, including requirements imposed by the chosen neighborhood and boundary condition. The resulting discrete scale space respects important topological invariants such as the Euler number, a key criterion for the successful implementation of algorithms operating on critical points in its deep structure. Relevant properties of the discrete diffusion equation and the Eigenvalue decomposition of its Laplacian kernel are discussed and a fast and robust sampling method is proposed. We finally discuss properties of topological graphs under the influence of smoothing, setting the stage for more robust deep structure extraction algorithms.

A new generalised α scale spaces quadrature filters

The α scale spaces is a recent theory that open new possibilities of phase-based image processing. It is a parameterised class (α∈]0,1]) of linear scale space representations, which allows a continuous connection beyond the well-known Gaussian scale space (α=1). In this paper, we make use of this unified representation to derive new families of band pass quadrature filters, built from derivatives and difference of the α scale space generating kernels. This construction leads to generalised α kernel filters including the commonly known families derived from the Gaussian and the Poisson kernels. The properties of each family are first studied and then experiments on one- and two-dimensional signals are shown to exemplify how the suggested filters can be used for edge detection. This work is complemented by an experimental evaluation, which demonstrates that the new proposed filters are a good alternative to the commonly used Log-Gabor filter.

Reduced-reference image quality assessment through SIFT intensity ratio

Scale invariant feature transform (SIFT) points are scale-space extreme points, representing local minutiae features in the Gaussian scale space. SIFT intensity ratio (SIR), as a novel reduced-reference metric, is feasible to assess various common distortions without the prior knowledge of distortion types. It describes relative changes in the number of SIFT points between a test image and its corresponding reference image. SIFT points in the metric are detected in the first octave of the difference-of-Gaussian scale space under certain preprocessings: neighborhood enhancement through a Laplacian operator to sharpen isolated points and thin edges, reducing false SIFT points; double-size image magnification through linear interpolation to amplify distortion effects, improving its sensitivity to image distortions. Experimental results demonstrate that SIR is superior to existing classic reduced-reference metrics, and can be used to assess different distortions.

Robust image salient regional extraction and matching based on DoGSS-MSERs

The current paper presents a robust image salient region extraction and matching algorithm based on the maximally stable extremal regions in the difference of Gaussian scale space (DoGSS-MSERs) combined with scale-invariant feature transform (SIFT) algorithm and the maximally stable extremal regions (MSERs) algorithm. First, the difference of Gaussian scale space (DoGSS) is constructed using image scale-space theory. The maximally stable extremal regions are then calculated and the stable component is extracted with blur-invariant and scale-invariant property using the stable method in the DoGSS. Finally, the regions are described with a novel region descriptor, thereby achieving matching. The experiments show that the feature regions extracted in the current paper inherit the good properties of SIFT and MSERs (scale-invariant and affine-invariant) and are more stable and more accurate for matching.

Singular integrals, scale-space and wavelet transforms

The Gaussian scale-space is a singular integral convolution operator with scaled Gaussian kernel. For a large class of singular integral convolution operators with differentiable kernels, a general method for constructing mother wavelets for continuous wavelet transforms is developed, and Calderón type inversion formulas, in both integral and semi-discrete forms, are derived for functions in Lp spaces. In the case of the Gaussian scale-space, the semi-discrete inversion formula can further be expressed as a sum of wavelet transforms with the even order derivatives of the Gaussian as mother wavelets. Similar results are obtained for B-spline scale-space, in which the high frequency component of a function between two consecutive dyadic scales can be represented as a finite linear combination of wavelet transforms with the derivatives of the B-spline or the spline framelets of Ron and Shen as mother wavelets.