Is it possible to use stereo images to generate point clouds and to compute rigorous uncertainty maps? Currently, neither modern commercial photogrammetric software nor state-of-the-art algorithms are able to provide a spatial distribution of uncertainty. In this letter, we explain why this is the case, despite a high demand from the user community. Many applications would indeed benefit from the availability of error bars on each point, as uncertainties on derived models and quantities could be accurately predicted. For instance, change detection could be performed rigorously since the statistical significance of observed changes could be computed. In this letter, we focus on dense stereo methods. We first explain that it is not possible to derive reliable predictive uncertainties mainly due to matching and modeling errors. Our research shows that both intrinsic and practical limitations of the algorithms lead to unpredictable artifacts. Then, we focus on the use of empirical errors, showing that, despite the redundancy brought by multiview stereo, there is a fundamental limitation due to the unknown density of independent measurements. We think that these problems will represent a big challenge for the future, as these limitations cannot be addressed by algorithmic design, computational power, or imaging sensor technology.

Topographic mapping is one of the main applications of airborne LiDAR. Waveform digitization and processing allow for both improved accuracy and higher ground detection rate compared with discrete return systems. Nevertheless, the quality of the ground peak estimation, based on last return extraction, strongly depends on the algorithm used. Best performing methods are too computationally intensive to be used on large data sets. We used Bayesian inference to develop a new ground extraction method whose most original feature is predictive uncertainty computation. It is also fast and robust to ringing and peak overlaps. Obtaining consistent ranging uncertainties is essential for determining the spatial distribution of error on the final product, point cloud, or digital elevation model. The robustness is achieved by a partial deconvolution followed by a Bayesian Gaussian function regression on optimally truncated data, which helps reduce the impact of overlapping peaks from low vegetation. Results from real data are presented, and the gain with respect to classical Gaussian peak fitting is assessed and illustrated.

In this paper, we propose a model-based approach for the multiresolution fusion of satellite images. Given the high-spatial-resolution panchromatic (Pan) image and the low-spatial- and high-spectral-resolution multispectral (MS) image acquired over the same geographical area, the problem is to generate a high-spatial- and high-spectral-resolution MS image. This is clearly an ill-posed problem, and hence, we need a proper regularization. We model each of the low-spatial-resolution MS images as the aliased and noisy version of their corresponding high spatial resolution, i.e., fused (to be estimated) MS images. A proper aliasing matrix is assumed to take care of the undersampling process. The high-spatial-resolution MS images to be estimated are then modeled as separate inhomogeneous Gaussian Markov random fields (IGMRF), and a maximuma posteriori(MAP) estimation is used to obtain the fused image for each of the MS bands. The IGMRF parameters are estimated from the available high-resolution Pan image and are used in the prior model for regularization purposes. Since the method does not directly operate on Pan pixel values as most of the other methods do, spectral distortion is minimum, and the spatial properties are better preserved in the fused image as the IGMRF parameters are learned at every pixel. We demonstrate the effectiveness of our approach over some existing methods by conducting experiments on synthetic data, as well as on the images captured by the QuickBird satellite.

We focus on a geophysical application of image processing: the measurement of high resolution ground deformation from two optical satellite images taken at different dates. Disparity maps estimated from image pairs usually lack quantitative error estimates. This is a major issue for measuring physical parameters, such as ground deformation or topography variations. Thus, we propose a new method to infer the disparity map. We adopt a probabilistic approach, treating all parameters as random variables, which provides a rigorous framework for parameter estimation and uncertainty evaluation. We start by defining a generative model of the data given all model variables. This forward model consists of warping the scene using B-Splines and applying a spatially adaptive radiometric change map. Then we use Bayesian inference to invert and recover the a posteriori probability density function (pdf) of the disparity map. The method is validated on multidate SPOT 5 imagery related to the Bam earthquake (Iran), showing results compatible with INSAR measurements.

In this paper we propose a model based approach for multi-resolution fusion of satellite images. Given the high spatial resolution panchromatic (Pan) image and a low spatial and high spectral resolution multi-spectral (MS) image of the same geographical area, the problem is to generate a high spatial and high spectral resolution multi-spectral image. This is clearly an ill-posed problem and hence we need a proper regularization. We model each of the low spatial resolution MS images as the aliased and noisy versions of their corresponding high spatial resolution i.e., fused (to be estimated) MS images. The decimation (aliasing) matrix for each of the MS images is automatically estimated from the data. The high spatial resolution MS images to be estimated are then modeled as separate inhomogeneous Gaussian Markov random fields (IGMRF) and a maximumaposteriori(MAP) estimation is used to obtain the fused image for each of the MS bands. The IGMRF parameters are estimated from the available high resolution Pan image and are used in the prior model for regularization purposes. Since the method does not directly operate on the Pan pixel values as most of the other methods do, the spectral distortion is minimum and the spatial properties are better preserved in the fused image as the IGMRF parameters are learnt at every pixel. We demonstrate the effectiveness of our approach over some existing methods by conducting the experiments on synthetic data as well as on real images.

The deconvolution of blurred and noisy satellite images is an ill-posed inverse problem, which can be regularized within a Bayesian context by using an a priori model of the reconstructed solution. Since real satellite data show spatially variant characteristics, we propose here to use an inhomogeneous model. We use the maximum likelihood estimator (MLE) to estimate its parameters and we show that the MLE computed on the corrupted image is not suitable for image deconvolution because it is not robust to noise. We then show that the estimation is correct only if it is made from the original image. Since this image is unknown, we need to compute an approximation of sufficiently good quality to provide useful estimation results. Such an approximation is provided by a wavelet-based deconvolution algorithm. Thus, a hybrid method is first used to estimate the space-variant parameters from this image and then to compute the regularized solution. The obtained results on high resolution satellite images simultaneously exhibit sharp edges, correctly restored textures, and a high SNR in homogeneous areas, since the proposed technique adapts to the local characteristics of the data.

In this paper we propose a new algorithm to estimate the parameters of the noise related to the sensor and the impulse response of the optical system, from a blurred and noisy satellite or aerial image. The noise is supposed to be white, Gaussian and stationary. The blurring kernel has a parametric form and is modeled in such a way as to take into account the physics of the system (the atmosphere, the optics and the sensor). The observed scene is described by a fractal model, taking into account the scale invariance properties of natural images. The estimation is performed automatically by maximizing a marginalized likelihood, which is achieved by a deterministic algorithm whose complexity is limited to O (N), where N is the number of pixels.

In this paper we present a new deconvolution method, able to deal with noninvertible blurring functions. To avoid noise amplification, a prior model of the image to be reconstructed is used within a Bayesian framework. We use a spatially adaptive prior defined with a complex wavelet transform in order to preserve shift invariance and to better restore variously oriented features. The unknown image is estimated by an EM technique, whose E step is a Landweber update iteration, and the M step consists of denoising the image, which is achieved by wavelet coefficient thresholding. The new algorithm has been applied to high resolution satellite and aerial data, showing better performance than existing techniques when the blurring process is not invertible, like motion blur for instance.

In this paper, we propose to use a hidden Markov tree modeling of the complex wavelet packet transform, to capture the inter-scale dependencies of natural images. First, the observed image, blurred and noisy, is deconvolved without regularization. Then its transform is denoised within a Bayesian framework using the proposed model, whose parameters are estimated by an EM technique. The total complexity of this new deblurring algorithm remains O(N).

The deconvolution of blurred and noisy satellite images is an ill-posed inverse problem. Donoho (1994) has proposed to deconvolve the image without regularization and to denoise the result in a wavelet basis by thresholding the transformed coefficients. We have developed a new filtering method, consisting of using a complex wavelet packet basis. Herein, the thresholding functions associated to the proposed method are automatically estimated. The estimation is performed within a Bayesian framework, by modeling the subbands using generalized Gaussian distributions, and by applying the maximum a posteriori (MAP) estimator on each coefficient. Compared to real wavelet-packet-based algorithms, the proposed method is shift invariant, provides good directionality properties and remains of complexity O(N).

The deconvolution of blurred and noisy satellite images is an ill-posed inverse problem, which can be regularized within a Bayesian context by using an a priori model of the reconstructed solution. Since real satellite data show spatially variant characteristics, we propose to use an inhomogeneous model. We use the maximum likelihood estimator (MLE) to estimate its parameters. We demonstrate that the MLE computed on the corrupted image is not suitable for image deconvolution, because it is not robust to noise. Then we show that the estimation is correct only if it is made from the original image. As this image is unknown, we need to compute an approximation of sufficiently good quality to provide useful estimation results. Such an approximation is provided by a wavelet-based deconvolution algorithm. Thus, an hybrid method is first used to estimate the space-variant parameters from this image and second to compute the regularized solution. The obtained results on high resolution satellite images simultaneously exhibit sharp edges, correctly restored textures and a high SNR in homogeneous areas, since the proposed technique adapts to the local characteristics of the data.