Showing papers in "IEEE Transactions on Image Processing in 1996"
TL;DR: This correspondence discusses an extension of the well-known phase correlation technique to cover translation, rotation, and scaling, which shows excellent robustness against random noise.
Abstract: 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.
1,939 citations
TL;DR: Application of the method to intersubject registration of neuroanatomical structures illustrates the ability to account for local anatomical variability.
Abstract: A general automatic approach is presented for accommodating local shape variation when mapping a two-dimensional (2-D) or three-dimensional (3-D) template image into alignment with a topologically similar target image. Local shape variability is accommodated by applying a vector-field transformation to the underlying material coordinate system of the template while constraining the transformation to be smooth (globally positive definite Jacobian). Smoothness is guaranteed without specifically penalizing large-magnitude deformations of small subvolumes by constraining the transformation on the basis of a Stokesian limit of the fluid-dynamical Navier-Stokes equations. This differs fundamentally from quadratic penalty methods, such as those based on linearized elasticity or thin-plate splines, in that stress restraining the motion relaxes over time allowing large-magnitude deformations. Kinematic nonlinearities are inherently necessary to maintain continuity of structures during large-magnitude deformations, and are included in all results. After initial global registration, final mappings are obtained by numerically solving a set of nonlinear partial differential equations associated with the constrained optimization problem. Automatic regridding is performed by propagating templates as the nonlinear transformations evaluated on a finite lattice become singular. Application of the method to intersubject registration of neuroanatomical structures illustrates the ability to account for local anatomical variability.
1,280 citations
TL;DR: A novel observation model based on motion compensated subsampling is proposed for a video sequence and Bayesian restoration with a discontinuity-preserving prior image model is used to extract a high-resolution video still given a short low-resolution sequence.
Abstract: The human visual system appears to be capable of temporally integrating information in a video sequence in such a way that the perceived spatial resolution of a sequence appears much higher than the spatial resolution of an individual frame. While the mechanisms in the human visual system that do this are unknown, the effect is not too surprising given that temporally adjacent frames in a video sequence contain slightly different, but unique, information. This paper addresses the use of both the spatial and temporal information present in a short image sequence to create a single high-resolution video frame. A novel observation model based on motion compensated subsampling is proposed for a video sequence. Since the reconstruction problem is ill-posed, Bayesian restoration with a discontinuity-preserving prior image model is used to extract a high-resolution video still given a short low-resolution sequence. Estimates computed from a low-resolution image sequence containing a subpixel camera pan show dramatic visual and quantitative improvements over bilinear, cubic B-spline, and Bayesian single frame interpolations. Visual and quantitative improvements are also shown for an image sequence containing objects moving with independent trajectories. Finally, the video frame extraction algorithm is used for the motion-compensated scan conversion of interlaced video data, with a visual comparison to the resolution enhancement obtained from progressively scanned frames.
1,058 citations
TL;DR: A new image multiresolution transform that is suited for both lossless (reversible) and lossy compression, and entropy obtained with the new transform is smaller than that obtained with predictive coding of similar complexity.
Abstract: We propose a new image multiresolution transform that is suited for both lossless (reversible) and lossy compression. The new transformation is similar to the subband decomposition, but can be computed with only integer addition and bit-shift operations. During its calculation, the number of bits required to represent the transformed image is kept small through careful scaling and truncations. Numerical results show that the entropy obtained with the new transform is smaller than that obtained with predictive coding of similar complexity. In addition, we propose entropy-coding methods that exploit the multiresolution structure, and can efficiently compress the transformed image for progressive transmission (up to exact recovery). The lossless compression ratios are among the best in the literature, and simultaneously the rate versus distortion performance is comparable to those of the most efficient lossy compression methods.
738 citations
TL;DR: A new framework for removing impulse noise from images is presented in which the nature of the filtering operation is conditioned on a state variable defined as the output of a classifier that operates on the differences between the input pixel and the remaining rank-ordered pixels in a sliding window.
Abstract: A new framework for removing impulse noise from images is presented in which the nature of the filtering operation is conditioned on a state variable defined as the output of a classifier that operates on the differences between the input pixel and the remaining rank-ordered pixels in a sliding window. As part of this framework, several algorithms are examined, each of which is applicable to fixed and random-valued impulse noise models. First, a simple two-state approach is described in which the algorithm switches between the output of an identity filter and a rank-ordered mean (ROM) filter. The technique achieves an excellent tradeoff between noise suppression and detail preservation with little increase in computational complexity over the simple median filter. For a small additional cost in memory, this simple strategy is easily generalized into a multistate approach using weighted combinations of the identity and ROM filter in which the weighting coefficients can be optimized using image training data. Extensive simulations indicate that these methods perform significantly better in terms of noise suppression and detail preservation than a number of existing nonlinear techniques with as much as 40% impulse noise corruption. Moreover, the method can effectively restore images corrupted with Gaussian noise and mixed Gaussian and impulse noise. Finally, the method is shown to be extremely robust with respect to the training data and the percentage of impulse noise.
676 citations
TL;DR: The analysis shows that standard regularization penalties induce space-variant local impulse response functions, even for space-invariant tomographic systems, which leads naturally to a modified regularization penalty that yields reconstructed images with nearly uniform resolution.
Abstract: This paper examines the spatial resolution properties of penalized-likelihood image reconstruction methods by analyzing the local impulse response. The analysis shows that standard regularization penalties induce space-variant local impulse response functions, even for space-invariant tomographic systems. Paradoxically, for emission image reconstruction, the local resolution is generally poorest in high-count regions. We show that the linearized local impulse response induced by quadratic roughness penalties depends on the object only through its projections. This analysis leads naturally to a modified regularization penalty that yields reconstructed images with nearly uniform resolution. The modified penalty also provides a very practical method for choosing the regularization parameter to obtain a specified resolution in images reconstructed by penalized-likelihood methods.
520 citations
TL;DR: It is demonstrated that an anisotrop diffusion is well posed when there exists a unique global minimum for the energy functional and that the ill posedness of a certain anisotropic diffusion is caused by the fact that its energy functional has an infinite number of global minima that are dense in the image space.
Abstract: In this paper, we analyze the behavior of the anisotropic diffusion model of Perona and Malik (1990). The main idea is to express the anisotropic diffusion equation as coming from a certain optimization problem, so its behavior can be analyzed based on the shape of the corresponding energy surface. We show that anisotropic diffusion is the steepest descent method for solving an energy minimization problem. It is demonstrated that an anisotropic diffusion is well posed when there exists a unique global minimum for the energy functional and that the ill posedness of a certain anisotropic diffusion is caused by the fact that its energy functional has an infinite number of global minima that are dense in the image space. We give a sufficient condition for an anisotropic diffusion to be well posed and a sufficient and necessary condition for it to be ill posed due to the dense global minima. The mechanism of smoothing and edge enhancement of anisotropic diffusion is illustrated through a particular orthogonal decomposition of the diffusion operator into two parts: one that diffuses tangentially to the edges and therefore acts as an anisotropic smoothing operator, and the other that flows normally to the edges and thus acts as an enhancement operator.
516 citations
TL;DR: This work proposes a new approach to statistically optimal image reconstruction based on direct optimization of the MAP criterion, which requires approximately the same amount of computation per iteration as EM-based approaches, but the new method converges much more rapidly.
Abstract: Over the past years there has been considerable interest in statistically optimal reconstruction of cross-sectional images from tomographic data. In particular, a variety of such algorithms have been proposed for maximum a posteriori (MAP) reconstruction from emission tomographic data. While MAP estimation requires the solution of an optimization problem, most existing reconstruction algorithms take an indirect approach based on the expectation maximization (EM) algorithm. We propose a new approach to statistically optimal image reconstruction based on direct optimization of the MAP criterion. The key to this direct optimization approach is greedy pixel-wise computations known as iterative coordinate decent (ICD). We propose a novel method for computing the ICD updates, which we call ICD/Newton-Raphson. We show that ICD/Newton-Raphson requires approximately the same amount of computation per iteration as EM-based approaches, but the new method converges much more rapidly (in our experiments, typically five to ten iterations). Other advantages of the ICD/Newton-Raphson method are that it is easily applied to MAP estimation of transmission tomograms, and typical convex constraints, such as positivity, are easily incorporated.
493 citations
TL;DR: A general framework for anisotropic diffusion of multivalued images is presented and the proposed framework is applied to the filtering of color images represented in CIE-L*a*b* space.
Abstract: A general framework for anisotropic diffusion of multivalued images is presented. We propose an evolution equation where, at each point in time, the directions and magnitudes of the maximal and minimal rate of change in the vector-image are first evaluated. These are given by eigenvectors and eigenvalues of the first fundamental form in the given image metric. Then, the image diffuses via a system of coupled differential equations in the direction of minimal change. The diffusion "strength" is controlled by a function that measures the degree of dissimilarity between the eigenvalues. We apply the proposed framework to the filtering of color images represented in CIE-L*a*b* space.
475 citations
TL;DR: In this paper, approximate expressions for the mean and variance of implicitly defined estimators of unconstrained continuous parameters are derived using the implicit function theorem, the Taylor expansion, and the chain rule.
Abstract: Many estimators in signal processing problems are defined implicitly as the maximum of some objective function. Examples of implicitly defined estimators include maximum likelihood, penalized likelihood, maximum a posteriori, and nonlinear least squares estimation. For such estimators, exact analytical expressions for the mean and variance are usually unavailable. Therefore, investigators usually resort to numerical simulations to examine the properties of the mean and variance of such estimators. This paper describes approximate expressions for the mean and variance of implicitly defined estimators of unconstrained continuous parameters. We derive the approximations using the implicit function theorem, the Taylor expansion, and the chain rule. The expressions are defined solely in terms of the partial derivatives of whatever objective function one uses for estimation. As illustrations, we demonstrate that the approximations work well in two tomographic imaging applications with Poisson statistics. We also describe a "plug-in" approximation that provides a remarkably accurate estimate of variability even from a single noisy Poisson sinogram measurement. The approximations should be useful in a wide range of estimation problems.
426 citations
TL;DR: A well-known space-adaptive regularization method for image restoration is extended, which effectively utilizes, among others, the piecewise smoothness of both the image and the PSF to solve the scale problem inherent to the cost function.
Abstract: The primary difficulty with blind image restoration, or joint blur identification and image restoration, is insufficient information. This calls for proper incorporation of a priori knowledge about the image and the point-spread function (PSF). A well-known space-adaptive regularization method for image restoration is extended to address this problem. This new method effectively utilizes, among others, the piecewise smoothness of both the image and the PSF. It attempts to minimize a cost function consisting of a restoration error measure and two regularization terms (one for the image and the other for the blur) subject to other hard constraints. A scale problem inherent to the cost function is identified, which, if not properly treated, may hinder the minimization/blind restoration process. Alternating minimization is proposed to solve this problem so that algorithmic efficiency as well as simplicity is significantly increased. Two implementations of alternating minimization based on steepest descent and conjugate gradient methods are presented. Good performance is observed with numerically and photographically blurred images, even though no stringent assumptions about the structure of the underlying blur operator is made.
TL;DR: A hierarchical planar curve descriptor is developed that decomposes a curve into components of different scales so that the coarsest scale components carry the global approximation information while the finer scale components contain the local detailed information.
Abstract: By using the wavelet transform, the authors develop a hierarchical planar curve descriptor that decomposes a curve into components of different scales so that the coarsest scale components carry the global approximation information while the finer scale components contain the local detailed information. They show that the wavelet descriptor has many desirable properties such as multiresolution representation, invariance, uniqueness, stability, and spatial localization. A deformable wavelet descriptor is also proposed by interpreting the wavelet coefficients as random variables. The applications of the wavelet descriptor to character recognition and model-based contour extraction from low SNR images are examined. Numerical experiments are performed to illustrate the performance of the wavelet descriptor.
TL;DR: Experimental and comparative results in image filtering show very good performance measures when the error is measured in the L*a*b* space, which is known as a space where equal color differences result in equal distances, and therefore, it is very close to the human perception of colors
Abstract: The processing of color image data using directional information is studied. The class of vector directional filters (VDF), which was introduced by the authors in a previous work, is further considered. The analogy of VDF to the spherical median is shown, and their relation to the spatial median is examined. Moreover, their statistical and deterministic properties are studied, which demonstrate their appropriateness in image processing. VDF result in optimal estimates of the image vectors in the directional sense; this is very important in the case of color images, where the vectors' direction signifies the chromaticity of a given color. Issues regarding the practical implementation of VDF are also considered. In addition, efficient filtering schemes based on VDF are proposed, which include adaptive and/or double-window structures. Experimental and comparative results in image filtering show very good performance measures when the error is measured in the L*a*b* space. L*a*b* is known as a space where equal color differences result in equal distances, and therefore, it is very close to the human perception of colors. Moreover, an indication of the chromaticity error is obtained by measuring the error on the Maxwell triangle; the results demonstrate that VDF are very accurate chromaticity estimators.
TL;DR: The error-resilient entropy code (EREC) is introduced as a method for adapting existing schemes to give increased resilience to random and burst errors while maintaining high compression.
Abstract: Many source and data compression schemes work by splitting the input signal into blocks and producing variable-length coded data for each block. If these variable-length blocks are transmitted consecutively, then the resulting coder is highly sensitive to channel errors. Synchronization code words are often used to provide occasional resynchronization at the expense of some added redundant information. This paper introduces the error-resilient entropy code (EREC) as a method for adapting existing schemes to give increased resilience to random and burst errors while maintaining high compression. The EREC has been designed to exhibit graceful degradation with worsening channel conditions. The EREC is applicable to many problems and is particularly effective when the more important information is transmitted near the start of each variable-length block and is not dependent on following data. The EREC has been applied to both still image and video compression schemes, using the discrete cosine transform (DCT) and variable-length coding. The results have been compared to schemes using synchronization code words, and a large improvement in performance for noisy channels has been observed.
IBM1
TL;DR: The sequential, lossless compression schemes obtained when the context modeler is used with an arithmetic coder, are tested with a representative set of gray-scale images and the compression ratios are compared with state-of-the-art algorithms available in the literature.
Abstract: Inspired by theoretical results on universal modeling, a general framework for sequential modeling of gray-scale images is proposed and applied to lossless compression. The model is based on stochastic complexity considerations and is implemented with a tree structure. It is efficiently estimated by a modification of the universal algorithm context. Several variants of the algorithm are described. The sequential, lossless compression schemes obtained when the context modeler is used with an arithmetic coder are tested with a representative set of gray-scale images. The compression ratios are compared with those obtained with state-of-the-art algorithms available in the literature, with the results of the comparison consistently favoring the proposed approach.
TL;DR: By using an error correction method that approximates the reconstructed coefficients quantization error, this work minimize distortion for a given compression rate at low computational cost.
Abstract: Schemes for image compression of black-and-white images based on the wavelet transform are presented. The multiresolution nature of the discrete wavelet transform is proven as a powerful tool to represent images decomposed along the vertical and horizontal directions using the pyramidal multiresolution scheme. The wavelet transform decomposes the image into a set of subimages called shapes with different resolutions corresponding to different frequency bands. Hence, different allocations are tested, assuming that details at high resolution and diagonal directions are less visible to the human eye. The resultant coefficients are vector quantized (VQ) using the LGB algorithm. By using an error correction method that approximates the reconstructed coefficients quantization error, we minimize distortion for a given compression rate at low computational cost. Several compression techniques are tested. In the first experiment, several 512/spl times/512 images are trained together and common table codes created. Using these tables, the training sequence black-and-white images achieve a compression ratio of 60-65 and a PSNR of 30-33. To investigate the compression on images not part of the training set, many 480/spl times/480 images of uncalibrated faces are trained together and yield global tables code. Images of faces outside the training set are compressed and reconstructed using the resulting tables. The compression ratio is 40; PSNRs are 30-36. Images from the training set have similar compression values and quality. Finally, another compression method based on the end vector bit allocation is examined.
TL;DR: Vector quantization (VQ) as mentioned in this paper provides a means of converting the decomposed signal into bits in a manner that takes advantage of remaining inter and intraband correlation as well as of the more flexible partitions of higher dimensional vector spaces.
Abstract: Subband and wavelet decompositions are powerful tools in image coding because of their decorrelating effects on image pixels, the concentration of energy in a few coefficients, their multirate/multiresolution framework, and their frequency splitting, which allows for efficient coding matched to the statistics of each frequency band and to the characteristics of the human visual system. Vector quantization (VQ) provides a means of converting the decomposed signal into bits in a manner that takes advantage of remaining inter and intraband correlation as well as of the more flexible partitions of higher dimensional vector spaces. Since 1988, a growing body of research has examined the use of VQ for subband/wavelet transform coefficients. We present a survey of these methods.
TL;DR: A more general set of steerable filters is presented that alleviate the problem of local orientation patterns in imagery that are periodic with period pi, independent of image structure.
Abstract: Steerable filters have been used to analyze local orientation patterns in imagery. Such filters are typically based on directional derivatives, whose symmetry produces orientation responses that are periodic with period /spl pi/, independent of image structure. We present a more general set of steerable filters that alleviate this problem.
TL;DR: A reliable and efficient computational algorithm for restoring blurred and noisy images that can be used in an adaptive/interactive manner in situations when knowledge of the noise variance is either unavailable or unreliable is proposed.
Abstract: A reliable and efficient computational algorithm for restoring blurred and noisy images is proposed. The restoration process is based on the minimal total variation principle introduced by Rudin et al. For discrete images, the proposed algorithm minimizes a piecewise linear l/sub 1/ function (a measure of total variation) subject to a single 2-norm inequality constraint (a measure of data fit). The algorithm starts by finding a feasible point for the inequality constraint using a (partial) conjugate gradient method. This corresponds to a deblurring process. Noise and other artifacts are removed by a subsequent total variation minimization process. The use of the linear l/sub 1/ objective function for the total variation measurement leads to a simpler computational algorithm. Both the steepest descent and an affine scaling Newton method are considered to solve this constrained piecewise linear l/sub 1/ minimization problem. The resulting algorithm, when viewed as an image restoration and enhancement process, has the feature that it can be used in an adaptive/interactive manner in situations when knowledge of the noise variance is either unavailable or unreliable. Numerical examples are presented to demonstrate the effectiveness of the proposed iterative image restoration and enhancement process.
TL;DR: The simultaneous MART algorithm (SMART) and the expectation maximization method for likelihood maximization (EMML) are extended to block-iterative versions, BI-SMART and BI-EMML, that converge to a solution in the feasible case, for any choice of subsets.
Abstract: The simultaneous MART algorithm (SMART) and the expectation maximization method for likelihood maximization (EMML) are extended to block-iterative versions, BI-SMART and BI-EMML, that converge to a solution in the feasible case, for any choice of subsets. The BI-EMML reduces to the "ordered subset" EMML of Hudson et al. (1992, 1994) when their "subset balanced" property holds.
TL;DR: This work quantifies "locality" and bound the locality of multidimensional space-filling curves, which comes close to achieving optimal locality.
Abstract: A space-filling curve is a linear traversal of a discrete finite multidimensional space. In order for this traversal to be useful in many applications, the curve should preserve "locality". We quantify "locality" and bound the locality of multidimensional space-filling curves. Classic Hilbert space-filling curves come close to achieving optimal locality.
TL;DR: An algorithm that generates a vertically aligned stereo pair by warped resampling is described, which uses grey scale image matching between the components of the stereo pair but confined to feature points.
Abstract: The assumption that epipolar lines are parallel to image scan lines is made in many algorithms for stereo analysis. If valid, it enables the search for corresponding image features to be confined to one dimension and, hence, simplified. An algorithm that generates a vertically aligned stereo pair by warped resampling is described. The method uses grey scale image matching between the components of the stereo pair but confined to feature points.
TL;DR: It is shown that the slant plane circular SAR, unlike theslant plane linear SAR, has the capability to extract three-dimensional imaging information of a target scene.
Abstract: This paper presents a method for imaging from the slant plane data collected by a synthetic aperture radar (SAR) over the full rotation or a partial segment of a circular flight path. A Fourier analysis for the Green's function of the imaging system is provided. This analysis is the basis of an inversion for slant plane circular SAR data. The reconstruction algorithm and resolution for this SAR system are outlined. It is shown that the slant plane circular SAR, unlike the slant plane linear SAR, has the capability to extract three-dimensional imaging information of a target scene. The merits of the algorithm are demonstrated via a simulated target whose ultra wideband foliage penetrating (FOPEN) or ground penetrating (GPEN) ultrahigh frequency (UHF) radar signature varies with the radar's aspect angle.
TL;DR: In this article, the Gaussian mixture density decomposition (GMDD) algorithm is proposed to identify each Gaussian component in the mixture and then decompose the mixture into a mixture of normal distributions.
Abstract: We present a new approach to the modeling and decomposition of Gaussian mixtures by using robust statistical methods. The mixture distribution is viewed as a contaminated Gaussian density. Using this model and the model-fitting (MF) estimator, we propose a recursive algorithm called the Gaussian mixture density decomposition (GMDD) algorithm for successively identifying each Gaussian component in the mixture. The proposed decomposition scheme has advantages that are desirable but lacking in most existing techniques. In the GMDD algorithm the number of components does not need to be specified a priori, the proportion of noisy data in the mixture can be large, the parameter estimation of each component is virtually initial independent, and the variability in the shape and size of the component densities in the mixture is taken into account. Gaussian mixture density modeling and decomposition has been widely applied in a variety of disciplines that require signal or waveform characterization for classification and recognition. We apply the proposed GMDD algorithm to the identification and extraction of clusters, and the estimation of unknown probability densities. Probability density estimation by identifying a decomposition using the GMDD algorithm, that is, a superposition of normal distributions, is successfully applied to automated cell classification. Computer experiments using both real data and simulated data demonstrate the validity and power of the GMDD algorithm for various models and different noise assumptions.
TL;DR: This work presents a unified approach to noise removal, image enhancement, and shape recovery in images that relies on the level set formulation of the curve and surface motion, which leads to a class of PDE-based algorithms.
Abstract: We present a unified approach to noise removal, image enhancement, and shape recovery in images. The underlying approach relies on the level set formulation of the curve and surface motion, which leads to a class of PDE-based algorithms. Beginning with an image, the first stage of this approach removes noise and enhances the image by evolving the image under flow controlled by min/max curvature and by the mean curvature. This stage is applicable to both salt-and-pepper grey-scale noise and full-image continuous noise present in black and white images, grey-scale images, texture images, and color images. The noise removal/enhancement schemes applied in this stage contain only one enhancement parameter, which in most cases is automatically chosen. The other key advantage of our approach is that a stopping criteria is automatically picked from the image; continued application of the scheme produces no further change. The second stage of our approach is the shape recovery of a desired object; we again exploit the level set approach to evolve an initial curve/surface toward the desired boundary, driven by an image-dependent speed function that automatically stops at the desired boundary.
TL;DR: A new lossless algorithm is presented that exploits the interblock correlation in the index domain to achieve significant reduction of bit rates without introducing extra coding distortion when compared to memoryless VQ.
Abstract: In memoryless vector quantization (VQ) for images, each block is quantized independently and its corresponding index is sent to the decoder. This paper presents a new lossless algorithm that exploits the interblock correlation in the index domain. We compare the current index with previous indices in a predefined search path, and then send the corresponding search order to the decoder. The new algorithm achieves significant reduction of bit rates without introducing extra coding distortion when compared to memoryless VQ. It is very simple and computationally efficient.
TL;DR: Solutions to the problem of matching and recognizing planar curves that are modeled by B-splines, independently of possible affine transformations to which the original curve has been subjected, are presented through the use of a new class of weighted B- splitting curve moments that are well defined for both open and closed curves.
Abstract: The article deals with the problem of matching and recognizing planar curves that are modeled by B-splines, independently of possible affine transformations to which the original curve has been subjected (for example, rotation, translation, scaling, orthographic, and semiperspective projections), and possible occlusion. It presents a fast algorithm for estimating the B-spline control points that is robust to nonuniform sampling, noise, and local deformations. Curve matching is achieved by using a similarity measure based on the B-spline knot points introduced by Cohen et al. (1991). This method, however, can neither handle the affine transformation between the curves nor the occlusion. Solutions to these two problems are presented through the use of a new class of weighted B-spline curve moments that are well defined for both open and closed curves. The method has been applied to classifying affine-transformed aircraft silhouettes, and appears to perform well.
TL;DR: A scheme that automatically selects the optimal features for each pixel using wavelet analysis is proposed, leading to a robust segmentation algorithm.
Abstract: The optimal features with which to discriminate between regions and, thus, segment an image often differ depending on the nature of the image. Many real images are made up of both smooth and textured regions and are best segmented using different features in different areas. A scheme that automatically selects the optimal features for each pixel using wavelet analysis is proposed, leading to a robust segmentation algorithm. An automatic method for determining the optimal number of regions for segmentation is also developed.
TL;DR: The test results showed that the developed method was effective in correcting the variations in RGB color values caused by vision system components, and most residual RGB errors were caused by residual nonuniformity of illumination in images.
Abstract: A color calibration method for correcting the variations in RGB color values caused by vision system components was developed and tested in this study. The calibration scheme concentrated on comprehensively estimating and removing the RGB errors without specifying error sources and their effects. The algorithm for color calibration was based upon the use of a standardized color chart and developed as a preprocessing tool for color image analysis. According to the theory of image formation, RGB errors in color images were categorized into multiplicative and additive errors. Multiplicative and additive errors contained various error sources-gray-level shift, a variation in amplification and quantization in camera electronics or frame grabber, the change of color temperature of illumination with time, and related factors. The RGB errors of arbitrary colors in an image were estimated from the RGB errors of standard colors contained in the image. The color calibration method also contained an algorithm for correcting the nonuniformity of illumination in the scene. The algorithm was tested under two different conditions-uniform and nonuniform illumination in the scene. The RGB errors of arbitrary colors in test images were almost completely removed after color calibration. The maximum residual error was seven gray levels under uniform illumination and 12 gray levels under nonuniform illumination. Most residual RGB errors were caused by residual nonuniformity of illumination in images, The test results showed that the developed method was effective in correcting the variations in RGB color values caused by vision system components.
TL;DR: The analysis of the multiscale morphological PDEs and of the eikonal PDE solved via weighted distance transforms are viewed as a unified area in nonlinear image processing, which is called differential morphology, and its potential applications to image processing and computer vision are discussed.
Abstract: Image processing via mathematical morphology has traditionally used geometry to intuitively understand morphological signal operators and set or lattice algebra to analyze them in the space domain. We provide a unified view and analytic tools for morphological image processing that is based on ideas from differential calculus and dynamical systems. This includes ideas on using partial differential or difference equations (PDEs) to model distance propagation or nonlinear multiscale processes in images. We briefly review some nonlinear difference equations that implement discrete distance transforms and relate them to numerical solutions of the eikonal equation of optics. We also review some nonlinear PDEs that model the evolution of multiscale morphological operators and use morphological derivatives. Among the new ideas presented, we develop some general 2-D max/min-sum difference equations that model the space dynamics of 2-D morphological systems (including the distance computations) and some nonlinear signal transforms, called slope transforms, that can analyze these systems in a transform domain in ways conceptually similar to the application of Fourier transforms to linear systems. Thus, distance transforms are shown to be bandpass slope filters. We view the analysis of the multiscale morphological PDEs and of the eikonal PDE solved via weighted distance transforms as a unified area in nonlinear image processing, which we call differential morphology, and briefly discuss its potential applications to image processing and computer vision.