Operational AVHRR navigation results

A navigation method that combine a precise image deformation model and an automatic adjustment on coastal landmarks is operationally used at the CMS on AVHRR imagery. This paper presents the principles of the method, the error sources and a detailed analysis of the results obtained in 1996-1997 with NOAA-14 and NOAA-12 images. Both ARGOS or TBUS orbital elements were used and yield similar results. The AVHRR image navigation without any landmark adjustment, is 3.9 km for NOAA-14 and 8.7 km for NOAA-12. The navigation error before ANA, which assumes a constant attitude error, is similar for NOAA-14, 3.5 km, but is greatly reduced for NOAA-12, 2.2 km. The NOAA-14 error is mainly due to clock error temporal variations, poorly known in real time, whereas the NOAA-12 error results from attitude errors of 5 mrad roll and 1.5 mrad yaw. The AVHRR image navigation error after landmark adjustment is 1.7 km. The landmark adjustment gives better performances on NOAA-14 images (with 60.1% success on the current orbit) than on NOAA-12 images (51.7% success); these values are increased to 88.9% for NOAA-14 and 84.0% for NOAA-12 when using the attitude estimated on the preceeding orbit.     

NOAA AVHRR image referencing

Abstract

A simple and fast algorithm for image referencing of the NOAA (National Oceanic and Atmospheric Administration) AVHRR (Advanced Very High Resolution Radiometer) data has been derived to facilitate the identification of geographic co-ordinates corresponding to any pixel on an NOAA image and vice versa. The procedure assumes a spherical Earth and circular orbit and takes into account the effects due to the Earth's rotation and oblateness and the scan skew. Inputs to the procedure are the ascending nodal longitude and lime, the time of the first scan line and one ground control point (GCP). The effects of an ellipsoid Earth and an elliptical orbit are corrected by using the GCP to adjust the spacecraft altitude and inclination angle. No detailed emphemeris data arc required. The average r.m.s. errors obtained by comparing with independent sets of well-distributed GCPs for each image are about 2 pixels and 2 lines or 3 km displacement. Results from the procedure are illustrated by the rectification of NOAA images over France.     

The occur-check problem revisited

A method is presented for executing PROLOG programs which avoids almost all unnecessary occur-checks. The method is based on a dynamic classification of the context in which logical variables occur. No static global analysis of the PROLOG program is required to detect the places where an occur-check has to be made. The presented method has also an important side benefit. It considerably cuts down on the number of memory references during the execution of PROLOG programs. Furthermore, in most cases it avoids “trailing” and “untrailing” of unbound variables altogether. Due to this fact the employed method actually speeds up PROLOG execution. The method is discussed in terms of an actual implementation based on the Warren abstract PROLOG instruction set. However, the method should be applicable to other implementation models as well. No assumptions are made with respect to particular hardware.     

SANA: Sub-pixel automatic navigation of AVHRR imagery

An automatic method (SANA) for sub-pixel navigation of Advanced Very High Resolution Radiometer (AVHRR) imagery is proposed. It progressively corrects satellite attitude and reduces navigation errors all over the scene by using an iterative approach. Tests performed on more than 400 AVHRR passes over Europe, demonstrate the above mentioned method capability to obtain, with no human intervention, a final navigation accuracy within 1 pixel. Main characteristics of such a method are its processing speed as well as its full exportability to other satellite packages.     

Optimal navigation in planar time-varying flow: Zermelo��s problem revisited

This paper is concerned with time-optimal navigation for flight vehicles in a planar, time-varying flow-field, where the objective is to find the fastest trajectory between initial and final points. The primary contribution of the paper is the observation that in a point-symmetric flow, such as inside vortices or regions of eddie-driven upwelling/downwelling, the rate of the steering angle has to be equal to one-half of the instantaneous vertical vorticity. Consequently, if the vorticity is zero, then the steering angle is constant. The result can be applied to find the time-optimal trajectories in practical control problems, by reducing the infinite-dimensional continuous problem to numerical optimization involving at most two unknown scalar parameters.     

An AVHRR mosaic image of Antarctica

Abstract

This project was started in October 1985 with the objectives of (1) producing a 1 km-resolution database of Antarctica and (2) producing a 1:5 000000 scale image map. So far, 28 three-band AVHRR scenes have been corrected for variable Sun reflectance and transformed to a polar stereographic projection using a digitized coastline for control. Relatively cloud-free segments from 18 scenes have been incorporated in a provisional mosaic and further segments are to be included to improve the picture.     

The periodic domino problem revisited

In this article, we give a new proof of the undecidability of the periodic domino problem. Compared to previous proofs, the main difference is that this one does not start from a proof of the undecidability of the (general) domino problem but only from the existence of an aperiodic tileset.     

The longest common subsequence problem revisited

This paper re-examines, in a unified framework, two classic approaches to the problem of finding a longest common subsequence (LCS) of two strings, and proposes faster implementations for both. Letl be the length of an LCS between two strings of lengthm andn ≥m, respectively, and let s be the alphabet size. The first revised strategy follows the paradigm of a previousO(ln) time algorithm by Hirschberg. The new version can be implemented in timeO(lm · min logs, logm, log(2n/m)), which is profitable when the input strings differ considerably in size (a looser bound for both versions isO(mn)). The second strategy improves on the Hunt-Szymanski algorithm. This latter takes timeO((r +n) logn), wherer≤mn is the total number of matches between the two input strings. Such a performance is quite good (O(n logn)) whenr～n, but it degrades to Θ(mn logn) in the worst case. On the other hand the variation presented here is never worse than linear-time in the productmn. The exact time bound derived for this second algorithm isO(m logn +d log(2mn/d)), whered ≤r is the number ofdominant matches (elsewhere referred to asminimal candidates) between the two strings. Both algorithms require anO(n logs) preprocessing that is nearly standard for the LCS problem, and they make use of simple and handy auxiliary data structures.     

The longest common subsequence problem revisited

This paper re-examines, in a unified framework, two classic approaches to the problem of finding a longest common subsequence (LCS) of two strings, and proposes faster implementations for both. Letl be the length of an LCS between two strings of lengthm andn m, respectively, and let s be the alphabet size. The first revised strategy follows the paradigm of a previousO(ln) time algorithm by Hirschberg. The new version can be implemented in timeO(lm · min logs, logm, log(2n/m)), which is profitable when the input strings differ considerably in size (a looser bound for both versions isO(mn)). The second strategy improves on the Hunt-Szymanski algorithm. This latter takes timeO((r +n) logn), wherermn is the total number of matches between the two input strings. Such a performance is quite good (O(n logn)) whenrn, but it degrades to (mn logn) in the worst case. On the other hand the variation presented here is never worse than linear-time in the productmn. The exact time bound derived for this second algorithm isO(m logn +d log(2mn/d)), whered r is the number ofdominant matches (elsewhere referred to asminimal candidates) between the two strings. Both algorithms require anO(n logs) preprocessing that is nearly standard for the LCS problem, and they make use of simple and handy auxiliary data structures.     

The normalized string editing problem revisited

Marzal and Vidal (1993) considered the problem of computing the normalized edit distance between two strings, and reported experimental results which demonstrated the use of the measure to recognize hand-written characters. Their paper formulated the theoretical properties of the measure and developed two algorithms to compute it. In this short communication the authors demonstrate how this measure is related to an auxiliary measure already defined in the literature-the inter-string constrained edit distance. Since the normalized edit distance can be computed efficiently using the latter, the analytic and experimental results reported in the above paper can be obtained just as accurately, but more efficiently, using the strategies presented here     

A new method for high accuracy navigation of NOAA AVHRR imagery

A method to produce rectified Advanced Very High Resolution Radiometer (AVHRR) datasets is proposed, using both the orbital model and identification of ground control points (GCPs), involving a single image transformation from the raw imagery. The ability of the orbital model to determine the geographical co-ordinates of pixels in a raw AVHRR image was tested, using a total of 1098 GCPs in 24 AVHRR images. Five of the 24 images were also rectified using the method proposed, using a newly identified set of GCPs. The differences between the geographical co-ordinates of the existing GCPs and those determined by the new method are calculated and discussed.     

Out-of-roundness problem revisited

The properties and computation of the minimum radial separation (MRS) standard for out-of-roundness are discussed. Another standard out-of-roundness measurement called the minimum area difference (MAD) center is introduced. Although the two centers have different characteristics, the approach to finding both centers shares many commonalities. An O(n log n+k) time algorithm which is used to compute the MRS center is presented. It also computes the MAD center of a simple polygon G, where n is the number of vertices of G, and k is the number of intersection points of the medial axis and the farthest-neighbor Voronoi diagram of G. The relationship between MRS and MAD is discussed     

The 2D lid-driven cavity problem revisited

Numerical simulations of the 2D lid-driven cavity flow are performed for a wide range of Reynolds numbers. Accurate benchmark results are provided for steady solutions as well as for periodic solutions around the critical Reynolds number. Numerous comparisons with the results available in the literature are given. The first Hopf bifurcation is localized by a study of the linearized problem.     

Using TBUS orbital elements for AVHRR image gridding

Abstract

The gridding method for computing the geographical position of Advanced Very High Resolution Radiometer image pixels is based on a model that takes as input the TBUS mean orbital elements and an improved value of a parameter giving mean satellite speed. An accurate speed value can be found if the satellite is close to the equator at subsequent TBUS times. The resultant gridding errors found by comparison with Svalbard coastlines are attributed to scan line timing and satellite attitude. Errors are corrected by parallel displacements and images gridded to 1-2 km accuracy are used for ice mapping in the Fram Strait.     

Systematic corrections of AVHRR image composites for temporal studies

For quantitative studies of vegetation dynamics, satellite data need to be corrected for spurious effects. In this study, we have applied several changes to an earlier advanced very high resolution radiometer (AVHRR) processing methodology (ABC3; [Remote Sens. Environ. 60 (1997) 35; J. Geophys. Res.-Atmos. 102 (1997) 29625; Can. J. Remote Sens. 23 (1997) 163]), to better represent the various physical processes causing contamination of the AVHRR measurements. These included published recent estimates of the NOAA-11 and NOAA-14 AVHRR calibration trajectories for channels 1 and 2; the best available estimates for the water vapour, aerosol and ozone amounts at the time of AVHRR data acquisition; an improved bidirectional reflectance algorithm that also takes into consideration surface topography; and an improved image screening algorithm for contaminated pixels. Unlike the previous study that compared the composite images to a single-date AVHRR image, we employed coincident TM images to approximate the AVHRR pixel field of view during the data acquisition. Compared to ABC3, the modified procedure ABC3V2 was found to improve the accuracy of AVHRR pixel reflectance estimates, both in the sensitivity (slope) of the regression and in r². The improvements were especially significant in AVHRR channel 1. In comparison with reference values derived from two full TM scenes, the corrected AVHRR surface reflectance estimates had average standard errors values of ±0.009 for AVHRR C1, ±0.019 for C2, and ±0.04 for NDVI; the corresponding r² values were 0.55, 0.80, and 0.50, respectively. The changes in ABC3V2 were not able to completely remove interannual variability for land cover types with little or no vegetation cover, which would be expected to remain stable over time, and they increased the interannual variability of mixed forest and grassland. These results are attributed to a combination of increased sensitivity to interannual dynamics on one hand, and the inability to remove all sources of noise for barren or sparsely vegetated northern land cover types on the other.     

Visual guided navigation for image retrieval

In this work, we are interested in technologies that will allow users to actively browse and navigate large image databases and to retrieve images through interactive fast browsing and navigation. The development of a browsing/navigation-based image retrieval system has at least two challenges. The first is that the system's graphical user interface (GUI) should intuitively reflect the distribution of the images in the database in order to provide the users with a mental picture of the database content and a sense of orientation during the course of browsing/navigation. The second is that it has to be fast and responsive, and be able to respond to users actions at an interactive speed in order to engage the users. We have developed a method that attempts to address these challenges of a browsing/navigation based image retrieval systems. The unique feature of the method is that we take an integrated approach to the design of the browsing/navigation GUI and the indexing and organization of the images in the database. The GUI is tightly coupled with the algorithms that run in the background. The visual cues of the GUI are logically linked with various parts of the repository (image clusters of various particular visual themes) thus providing intuitive correspondences between the GUI and the database contents. In the backend, the images are organized into a binary tree data structure using a sequential maximal information coding algorithm and each image is indexed by an n-bit binary index thus making response to users’ action very fast. We present experimental results to demonstrate the usefulness of our method both as a pre-filtering tool and for developing browsing/navigation systems for fast image retrieval from large image databases.     

The limitedness problem on distance automata: Hashiguchi''s method revisited

Hashiguchi has studied the limitedness problem of distance automata (DA) in a series of paper [(J. Comput System Sci. 24 (1982) 233; Theoret. Comput. Sci. 72 (1990) 27; Theoret. Comput. Sci. 233 (2000) 19)]. The distance of a DA can be limited or unbounded. Given that the distance of a DA is limited, Hashiguchi has proved in Hashiguchi (2000) that the distance of the automaton is bounded by 2^{4n3+nlg(n+2)+n}, where n is the number of states. In this paper, we study again Hashiguchi's solution to the limitedness problem. We have made a number of simplification and improvement on Hashiguchi's method. We are able to improve the upper bound to 2^{3n3+nlgn+n−1}.