Spectral Mixture Analysis is a widely used image analysis tool with many applications. Yet, one of the major issues with
this technique remains the lack of ability to properly account for the spectral variability of endmembers or ground cover
components that occur throughout an image scene. Endmember variability is most often addressed using iterative
mixture cycles (e.g. MESMA) in which different endmember combination models are compared for each pixel. The
model with the best fit is assigned to the pixel. The drawback of MESMA is the computational burden which often
hampers the operational use. In an attempt to address this issue we proposed a new geometric based methodology to
more efficiently evaluate different endmember combinations in MESMA. This geometric unmixing methodology has a
two-fold benefit. First of all, geometric unmixing allows a fast and fully constrained unmixing, which was previously
unfeasible in MESMA due to the long processing times of the available fully constrained unmixing methods. Secondly,
whereas the traditional MESMA explores all different endmember combinations separately, and selects the most
appropriate combination as a final step, our approach selects the best endmember combination prior to unmixing, as such
increasing the computational efficiency of MESMA. To do so, we built upon the equivalence between the reconstruction
error in least-squares unmixing and spectral angle minimization in geometric unmixing. With the inclusion of the
proposed endmember combination selection technique, the computation time decreased by a factor between 5 and 8.5,
depending on the size and organization of the libraries. The spectral angle can as such be used as a proxy for model fit,
enabling the selection of the proper endmember combination from large spectral libraries prior to unmixing.
KEYWORDS: Luminescence, Microscopy, Nerve, Signal to noise ratio, In vivo imaging, Sensors, Pre-clinical research, Video, Image registration, Visualization
Peripheral neuropathy can be caused by diabetes or AIDS or be a side-effect of chemotherapy. Fibered Fluorescence Microscopy (FFM) is a recently developed imaging modality using a fiber optic probe connected to a laser scanning unit. It allows for in-vivo scanning of small animal subjects by moving the probe along the tissue surface. In preclinical research, FFM enables non-invasive, longitudinal in vivo assessment of intra epidermal nerve fibre density in various
models for peripheral neuropathies. By moving the probe, FFM allows visualization of larger surfaces, since, during the
movement, images are continuously captured, allowing to acquire an area larger then the field of view of the probe. For analysis purposes, we need to obtain a single static image from the multiple overlapping frames. We introduce a mosaicing procedure for this kind of video sequence. Construction of mosaic images with sub-pixel alignment is indispensable and must be integrated into a global consistent image aligning. An additional motivation for the mosaicing is the use of overlapping redundant information to improve the signal to noise ratio of the acquisition, because the individual frames tend to have both high noise levels and intensity inhomogeneities. For longitudinal analysis, mosaics captured at different times must be aligned as well. For alignment, global correlation-based matching is compared with interest point matching. Use of algorithms working on multiple CPU's (parallel processor/cluster/grid) is imperative for use in a screening model.
KEYWORDS: Quantization, Image segmentation, Medical imaging, Magnetic resonance imaging, Tissues, Image filtering, Linear filtering, 3D image processing, Image processing, Signal attenuation
Bias field reduction is a common problem in medical imaging. A bias field usually manifests itself as a smooth intensity variation across the image. The resulting image inhomogeneity is a severe problem for posterior image processing and analysis techniques such as registration or segmentation. In this paper, we present a fast debiasing technique based on localized Lloyd-Max quantization. Thereby, the local bias is modelled as a multiplicative field and is assumed to be slowly varying. The method is based on the assumption that the local, undegraded histogram is characterized by a limited number of gray values. The goal is then to find the discrete intensity values such that spreading those values according to the local bias field reproduces the global histogram as good as possible. We show that our method is capable of efficiently reducing (even strong) bias fields in 3D volumes in only a few seconds.
KEYWORDS: Wavelets, Expectation maximization algorithms, Image restoration, Denoising, Principal component analysis, Deconvolution, Global system for mobile communications, Fourier transforms, Wavelet transforms, Signal to noise ratio
In this paper we study the restoration of multicomponent images, and more particularly, the effects of taking into account the dependencies between the image components. The used method is an expectation-maximization algorithm, which applies iteratively a deconvolution and a denoising step. It exploits the Fourier transform's economical noise representation for deconvolution, and the wavelet transform's economical representation of piecewise smooth images for denoising. The proposed restoration procedure performs wavelet shrinkage in a Bayesian denoising framework by applying multicomponent probability density models for the wavelet coefficients that fully account for the intercomponent correlations. In the experimental section, we compare our multicomponent procedures to its single-component counterpart. The results show that the methods using a multicomponent model and especially the one using the Gaussian scale mixture model, perform better than the single-component procedure.
KEYWORDS: Wavelets, Denoising, Global system for mobile communications, Signal to noise ratio, Remote sensing, Data modeling, Image fusion, Image filtering, Wavelet transforms, Statistical modeling
In this paper, we study denoising of multicomponent images. We present a framework of spatial wavelet-based
denoising techniques, based on Bayesian least-squares optimization procedures, using prior models for the wavelet
coefficients that account for the correlations between the image components. Within this framework, multicomponent
prior models for the wavelet coefficients are required that a) fully account for the interband correlations
between the image components, and b) approximate well the marginal distributions of the wavelet coefficients.
For this, multicomponent heavy tailed models are applied. We analyze three mixture priors: Gaussian scale
mixture (GSM) models, Laplacian mixture models and Bernoulli-Gaussian mixture models. As an extension of
the Bayesian framework, we propose a framework that also accounts for the correlation between the multicomponent
image and an auxiliary noise-free image, in order to improve the SNR of the first. For this, a GSM prior
model was applied. Experiments are conducted in the domain of remote sensing in both, simulated and real
noisy conditions.
A technique is presented for detecting vegetation crop nutrient stress from hyperspectral data. Experiments are conducted on peach trees. It is shown that nutrient deficiencies that caused stress could an be detected reliably on hyperspectral spectra. During an extensive field campaign, foliar and crown reflectance has been measured with a portable field spectroradiometer. Airborne hyperspectral imagery is acquired over the orchard with the AHS hyperspectral sensor. The multi-level approach (leaf level and top of canopy) enabled the assessment of vegetation indices and their relationship with pigment concentration at both leaf and canopy levels, showing the potential and limitations of hyperspectral remote sensing on the different levels. Stress on the peach orchard is was treated with iron chelates to recover from iron chlorosis conditions. Blocks of trees treated with iron chelates created a dynamic range of chlorophyll concentration as measured in leaves. A relationship is obtained between the measured spectra and estimated biochemical parameters via inversion of a linked directional homogeneous canopy reflectance model (ACRM) and the PROSPECT leaf model. Numerical model inversion was conducted by minimizing the difference between the measured reflectance samples and modeled values. An improved optimization method is presented. Results are compared with a simple linear regression analysis, linking chlorophyll to the reflectance measured at the leaf level and Top of Canopy (TOC). Optimal band regions and bandwidths are analyzed.
In this paper, we propose a segmentation algorithm for multi-component images. The technique is based on the combination of three principles: it is an interband approach, where the correlations between the different image components are exploited; it is a multi-resolution technique, that is applied in the wavelet domain; it
is a model based segmentation technique, that applies a multinormal model for the multi-component image, where model parameters are estimated using Maximum Likelihood principles. From this procedure, a regionmerging segmentation technique emerges, employing a generalized likelihood ratio test for the merging. The procedure is embedded into a larger segmentation framework for multi-component images. This framework contains anisotropic diffusion noise filtering, watershed-based segmentation and a multiscale region merging procedure. All techniques are multiscale procedures and work in the wavelet domain. Moreover, they all are multicomponent techniques, making use of the correlation in between the different image components. To demonstrate the proposed procedure, it is applied to a 3-band color image.
In this paper, a wavelet-based enhancement method for multicomponent images or image series is proposed. The method applies Bayesian estimation, including the use of a high-resolution noise-free grey scale image as prior information. The resulting estimator statistically exploits the correlation between the image series and the high-resolution noise-free image to enhance (i.e. to improve the signal to noise ratio and the spatial resolution) of the image series. To validate and demonstrate the procedure, results are shown on a color image. The idea of using an auxiliary image can be applied in many different domains. As an example, experiments are conducted in two different application domains: resolution enhancement of multispectral remote sensing images and improvement of brain activity measurements on functional MRI image time series.
KEYWORDS: Vegetation, Binary data, Sensors, Statistical analysis, Image classification, Point spread functions, Hyperspectral imaging, Data acquisition, Matrices, RGB color model
Hyperspectral image classification impose challenging requirements to
a classifier. It is well known that more spectral bands can be difficult to process and introduce problems such as the Hughes phenomenon. Nevertheless, user requirements are very demanding, as expectations grow with the available number of spectral bands: subtle differences in a large number of classes must be distinguished. As multiclass classifiers become rather complex for a large number of classes, a combination of binary classification results are often used to come to a class decision. In this approach, the posterior probability is retained for each of the binary classifiers. From these, a combined posterior probability for the multiclass case is obtained. The proposed technique is applied to map the highly diverse Belgian coastline. In total, 17 vegetation types are defined. Additionally, bare soil, shadow, water and urban area are also classified. The posterior probabilities are used for unmixing. This is demonstrated for 4 classes: bare soil and 3 vegetation classes. Results are very promosing, outperforming other approaches such as linear unmixing.
We study an image denoising approach the core of which is a locally adaptive estimation of the probability that a given coefficient contains a significant noise-free component, which we call "signal of interest". We motivate this approach within the minimum mean squared error criterion and develop and analyze different locally adaptive versions of this method for color and for multispectral images in remote sensing. For color images, we study two different approaches: (i) using a joint spatial/spectral activity indicator in the RGB color space and (ii) componentwise spatially adaptive denoising in a luminance-chrominance space. We demonstrate and discuss the advantages of both of these approaches in different scenarios. We also compare the analyzed method to other recent wavelet domain denoisers for multiband data both on color and on multispectral images.
This paper studies the detection of vegetation stress in orchards via remote sensing. During previous research, it was shown that stress can be detected reliably on hyperspectral reflectances of the fresh leaves, using a generic wavelet based hyperspectral classification. In this work, we demonstrate the capability to detect stress from airborne/spaceborne hyperspectral sensors by upscaling the leaf reflectances to top of atmosphere (TOA) radiances. Several data sets are generated, measuring the foliar reflectance with a portable field spectroradiometer, covering different time periods, fruit variants and stress types. We concentrated on the Jonagold and Golden Delicious apple trees, induced with mildew and nitrogen deficiency. First, a directional homogeneous canopy reflectance model (ACRM) is applied on these data sets for simulating top of canopy (TOC) spectra. Then, the TOC level is further upscaled to TOA, using the atmospheric radiative transfer model MODTRAN4. To simulate hyperspectral imagery acquired with real airborne/spaceborne sensors, the spectrum is further filtered and subsampled to the available resolution. Using these simulated upscaled TOC and TOA spectra in classification, we will demonstrate that there is still a differentiation possible between stresses and non-stressed trees. Furthermore, results show it is possible to train a classifier with simulated TOA data, to make a classification of real hyperspectral imagery over the orchard.
In this work, a wavelet representation of multivalued images is presented. The representation is based on a multiresolution extension of the First Fundamental Form that accesses gradient information of vector-valued images. With the extension, multiscale edge information of multivalued images is extracted. Moreover, a wavelet representation is obtained that, after inverse transformation, accumulates all edge information in a single greylevel image. In this work, a redundant wavelet representation is presented using dyadic wavelet frames. It is then extended towards orthogonal wavelet bases using the Discrete Wavelet Transformation (DWT). The representation is shown to be a natural framework for image fusion. An algorithm is presented for fusion of multispectral images.
KEYWORDS: Wavelets, Vegetation, Discrete wavelet transforms, Reflectivity, Feature extraction, Feature selection, Remote sensing, FDA class I medical device development, Statistical analysis, Linear filtering
The high spectral and high spatial resolution, intrinsic to hyperspectral remote sensing, result in huge quantities of data, which slows down the data processing and can result in a poor performance of classifiers. To improve the classification performance, efficient feature extraction methods are needed. This paper introduces a set of features based on the discrete wavelet transform (DWT). Wavelet coefficients, wavelet energies and wavelet detail histogram features are employed as new features for classification. As a feature reduction procedure, we propose a sequential floating search method. Selection is performed using a cost function based on the estimated probability of error, using the Fisher criterion. This procedure selects the best combination of features. To demonstrate the proposed wavelet features and selection procedure, we apply it to vegetation stress detection. For this application, it is shown that wavelet coefficients outperform spectral reflectance and that the proposed selection procedure outperforms combining the best single features.
In this paper a denoising technique for multispectral images exploiting interband correlations is proposed. A redundant wavelet transform is applied and denoising is applied by thresholding
wavelet coefficients. A scale adaptive threshold value is obtained by exploiting the interband correlation of the signal. First, the coefficients from different bands are multiplied. For these products, the signal and noise probability density functions (pdf) become more separated. The high signal correlation between bands is exploited further by summing these products over all bands, in this way separating noise and signal pdfs even more. The noise pdf of the proposed quantities is derived analytically and from this, a wavelet threshold is derived. The technique is demonstrated to outperform single band wavelet thresholding on multispectral remote sensing images.
We study cross-media image reproduction by constructing a tonal range mapping model. We aim at making reproductions that optimally represent the overall appearance of the originals despite a reduction in dynamic range. We propose a general mapping that works for all input and output white and black points. It is described by a two parameter functional model. The parameters are chosen so that one primarily corresponds to black point variations and the other to white point variations.
We set up psychometric experiments to estimate optimal parameter values. Paired comparison was employed because of its ease of use and accurate results. To keep the number of observations down, a small pilot experiment marks out a narrower range of values first. Furthermore, the two parameter optimisation is split into a sequential single parameter optimisation. The experiments are repeated for different white and black points. The model is completed by interpolating between the experimental points and determining the correlation between the parameters. A separate verification experiment proves the validity of the model within the experimental accuracy.
A comparison of our model with the CIECAM97s colour appearance model clarifies the fundamental difference between them. The tonal mapping model aims at the best overall reproduction of images. It produces more pleasing images by giving them higher overall contrast, whereas CIECAM faithfully models the appearance.
In this paper the fusion of multimodal images into one greylevel image is aimed at. A multiresolution technique, based on the wavelet multiscale edge representation is applied. The fusion consists of retaining only the modulus maxima of the wavelet coefficients from the different bands and combining them. After reconstruction, a synthetic image is obtained that contains the edge information from all bands simultaneously. Noise reduction is applied by removing the noise-related modulus maxima. In several experiments on test images and multispectral satellite images, we demonstrate that the proposed technique outperforms mapping techniques, as PCA and SOM and other wavelet-based fusion techniques.
The aim of this work is the development of a non-invasive technique for efficient and accurate volume quantization of the cerebellum of mice. This enables an in-vivo study on the development of the cerebellum in order to define possible alterations in cerebellum volume of transgenic mice. We concentrate on a semi-automatic segmentation procedure to extract the cerebellum from 3D magnetic resonance data. The proposed technique uses a 3D variant of Vincent and Soille's immersion based watershed algorithm which is applied to the gradient magnitude of the MR data. The algorithm results in a partitioning of the data in volume primitives. The known drawback of the watershed algorithm, over-segmentation, is strongly reduced by a priori application of an adaptive anisotropic diffusion filter on the gradient magnitude data. In addition, over-segmentation is a posteriori contingently reduced by properly merging volume primitives, based on the minimum description length principle. The outcome of the preceding image processing step is presented to the user for manual segmentation. The first slice which contains the object of interest is quickly segmented by the user through selection of basic image regions. In the sequel, the subsequent slices are automatically segmented. The segmentation results are contingently manually corrected. The technique is tested on phantom objects, where segmentation errors less than 2% were observed. Three-dimensional reconstructions of the segmented data are shown for the mouse cerebellum and the mouse brains in toto.
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