We expand upon the maximum likelihood inversion approach presented in Flynn, Tabb, and Carande ["Direct estimation of vegetation parameters from covariance data in polarimetric SAR interferometry", IGARSS 2002], and show how to optimally combine the polarimetric channels to form a bare earth estimate for the case of single layer ground scattering. In addition, for the two layer randomly oriented volume over ground (RV+G) scattering model, we show how to optimally recover the canopy structural parameters (bare earth and tree height) as well as the ground and volume backscatter polarimetric covariance matrices. This approach outperforms other techniques in terms of both estimation accuracy and computational complexity

Previous analysis of PolInSAR coherence regions (1) has shown that oftentimes a relatively small portion of the polarization space may account for a disproportionately large portion of the coherence region (Figure 1). Current vegetation scattering models (RV+G, OV+G)(2-3) typically only consider volume decorrelation effects, and cannot adequately account for this phenomenon. This paper investigates the effects of SNR decorrelation, estimation bias, and to a lesser extent, temporal decorrelation on the coherence region. I. NOISE ESTIMATION The RV/OV+G scattering models predict a convex coherence region that is highly eccentric. Assuming a diagonal noise covariance matrix, noise affects only the coherence amplitude, not the phase, with polarizations yielding low backscatter power being more decorrelated than polarizations yielding stronger return. Since the ground surface is typically strongly polarized at both L-band and P-band, fairly significant power variation (> 10 dB) often occurs throughout the coherence region. Since the coherence region is obtained by embedding a 4-D polarization subspace into a 2-D plane, significant redundancy exists at most points in the coherence region, i.e., multiple polarizations will yield the same coherence point. If such polarizations have different backscatter power, then the main effect of noise decorrelation on the coherence region is to fatten the coherence region in amplitude, with the outer portion of the coherence region boundary having higher power than the inner portion of the boundary. Although this provides a potential explanation for the behavior observed in Figure 1, a similar analysis reveals that any polarization dependent temporal decorrelation also yields much the same result. As a result, we investigate a noise decorrelation estimation algorithm in order to evaluate the degree to which SNR decorrelation is the dominant factor. Using an additive noise model, the observed PolInSAR covariance matrix, ˆ R , is given by

Polarimetric SAR interferometry (POLINSAR) is an emerging technique for the characterization of volumetric scattering processes. Each pixel of a POLINSAR interferogram is a 6/spl times/6 matrix of complex sample covariances among the polarimetric channels in the image pair. A model of polarimetric scattering from vegetation specifies the expected covariance matrix as a function of the vegetation parameters. The data matrix obeys a complex Wishart probability distribution that depends on the expected covariance. Using this, one can rind the maximum-likelihood estimate of the parameters from the data matrix. This paper presents the formula for the expected covariance matrix, as predicted by the model of Treuhaft and Siqueira for a random canopy over flat ground. An algorithm for computing the maximum-likelihood parameter estimate is derived. We test the algorithm on simulated data and compare its results to estimates derived from coherence samples. We conclude by discussing the extension of the direct estimation technique to more general POLINSAR scattering models.

Polarimetric SAR interferometry (POLINSAR) provides volumetric information about electromagnetic scattering processes, whereas standard INSAR assumes that only surface scattering is present. Instead of a single complex interferometric coherence for each pixel, POLINSAR observes a polarization-dependent coherence function whose range is called the coherence region. To estimate canopy parameters, the shape of this region must be matched to predictions from scattering models. For computational efficiency, the region must be represented by a small number of samples. Current sampling methods find the stationary points of coherence magnitude or phase; it is questionable whether the coherence region can be characterized adequately with so few samples. We have developed an algorithm for sampling the outer boundary of the coherence region. We formulate the problem of finding the minimum and maximum real part of the coherence as an eigenvalue problem. The solutions specify two points on the boundary. Other points are found by applying a phase shift to the POLINSAR cross-correlation matrix. The mathematical literature shows that the coherence region is convex, and hence the algorithm rinds the entire boundary. We present a comparison of boundary sampling to standard methods on L-band POLINSAR data from the SIR-C platform. It is evident that boundary sampling describes the shape of the coherence region more thoroughly than other methods.

Effective exploitation of polarimetric SAR interferometry data over vegetated areas requires the use of a vegetation model of sufficient complexity to capture the underlying scattering processes. The standard Treuhaft model (randomly oriented vegetation + ground) makes a number of assumptions that may not be true in general. This paper presents a two-layer extended model that allows canopy attenuation to be a function of polarization, does not require the canopy to extend all the way to the ground, and allows the ground to be sloped. It is shown that many cases exist in which the two models predict similar coherence region shapes for significantly different structural parameters. It is argued that a minimum of two baselines is required for robust model selection and inversion.

We present an algorithm for extracting and classifying two-dimensional motion in an image sequence based on motion trajectories. First, a multiscale segmentation is performed to generate homogeneous regions in each frame. Regions between consecutive frames are then matched to obtain two-view correspondences. Affine transformations are computed from each pair of corresponding regions to define pixel matches. Pixels matches over consecutive image pairs are concatenated to obtain pixel-level motion trajectories across the image sequence. Motion patterns are learned from the extracted trajectories using a time-delay neural network. We apply the proposed method to recognize 40 hand gestures of American Sign Language. Experimental results show that motion patterns of hand gestures can be extracted and recognized accurately using motion trajectories.

This paper is concerned with the detection of low-level structure in images. It describes an algorithm for image segmentation at multiple scales. The detected regions are homogeneous and surrounded by closed edge contours. Previous approaches to multiscale segmentation represent an image at different scales using a scale-space. However, structure is only represented implicitly in this representation, structures at coarser scales are inherently smoothed, and the problem of structure extraction is unaddressed. This paper argues that the issues of scale selection and structure detection cannot be treated separately. A new concept of scale is presented that represents image structures at different scales, and not the image itself. This scale is integrated into a nonlinear transform which makes structure explicit in the transformed domain. Structures that are stable (locally invariant) to changes in scale are identified as being perceptually relevant. The transform can be viewed as collecting spatially distributed evidence for edges and regions, and making it available at contour locations, thereby facilitating integrated detection of edges and regions without restrictive models of geometry or homogeneity. In this sense, it performs Gestalt analysis. All scale parameters of the transform are automatically determined, and the structure of any arbitrary geometry can be identified without any smoothing, even at coarse scales.

This paper presents a new technique for the estimation of 2D motion fields from image sequences. Homogeneous regions are identified and matched using a multiscale segmentation algorithm. Many matching difficulties result from structural changes in an image which occur only at certain scales and, hence, a multiscale approach results in a denser set of matched regions. Pixel correspondences are then obtained by estimating an affine transformation between matched regions. A motion field is then calculated from these correspondences. Areas where occlusion is present are identified and the effects of the occlusion on the affine parameter estimation process are compensated, resulting in a more accurate estimated motion field.