The use of hyperspectral remote sensing to assess vascular plant species richness on Horn Island,Mississippi

Relationships of plant species richness with spectral indices derived from airborne hyperspectral image data were evaluated for several habitat-types on Horn Island, Mississippi, northern Gulf of Mexico. A 126-band hyperspectral data cube of Horn Island acquired by the HyMap imaging system covered the 450–2500 nm spectrum at a 3 m Ground Sample Distance (GSD). Reflectance spectra were extracted from 5–11 HyMap pixels representing each of 95, 15-m vegetation line transects that were established randomly on the island. In simple regressions, no index related to richness when data from all habitat-types were combined. However, a number of reflectance and spectral derivative indices related significantly (p ≤ 0.05) with richness when habitat-types were considered separately. Only those indices which passed a fidelity test based on the consistency of index response to changes in plant and environmental moisture were selected as potentially reliable indicators of richness. Transect coefficient of variation (CV) for R₁₀₅₆/R₉₆₆ and R₉₂₀/R₈₃₄ related negatively with richness in meadows and transition zones, respectively. The CV of R₉₅₁/R₁₁₀₀ and R₉₀₄ related negatively with woodland richness. Negative regression slopes, field observations and spectral mixtures indicated that richness in these habitats declined with increased bare soil exposure. In marsh habitat, positive relationships of richness with mean R₆₁₈/R₂₄₇₅ or the CV of R₅₁₄/R₂₄₅₉ were explained by the increasing presence and patchy distribution of broadleaved vegetation in the progression from wetter, low-richness sites to slightly-elevated, higher-richness sites. Present results combined with those of a previous grassland study suggested that remotely-sensed indicators of soil exposure may be generally useful in the assessment of plant species richness in mesic habitats.     

Cluster analysis of hyperspectral optical data for discriminating phytoplankton pigment assemblages in the open ocean

Optical measurements including remote sensing provide a potential tool for the identification of dominant phytoplankton groups and for monitoring spatial and temporal changes in biodiversity in the upper ocean. We examine the application of an unsupervised hierarchical cluster analysis to phytoplankton pigment data and spectra of the absorption coefficient and remote-sensing reflectance with the aim of discriminating different phytoplankton assemblages in open ocean environments under non-bloom conditions. This technique is applied to an optical and phytoplankton pigment data set collected at several stations within the eastern Atlantic Ocean, where the surface total chlorophyll-a concentration (TChla) ranged from 0.11 to 0.62 mg m^− 3. Stations were selected on the basis of significant differences in the ratios of the two most dominant accessory pigments relative to TChla, as derived from High Performance Liquid Chromatography (HPLC) analysis. The performance of cluster analysis applied to absorption and remote-sensing spectra is evaluated by comparisons with the cluster partitioning of the corresponding HPLC pigment data, in which the pigment-based clusters serve as a reference for identifying different phytoplankton assemblages. Two indices, cophenetic and Rand, are utilized in these comparisons to quantify the degree of similarity between pigment-based and optical-based clusters. The use of spectral derivative analysis for the optical data was also evaluated, and sensitivity tests were conducted to determine the influence of parameters used in these calculations (spectral range, smoothing filter size, and band separation). The results of our analyses indicate that the second derivative calculated from hyperspectral (1 nm resolution) data of the phytoplankton absorption coefficient, a_ph(λ), and remote-sensing reflectance, R_rs(λ), provide better discrimination of phytoplankton pigment assemblages than traditional multispectral band-ratios or ordinary (non-differentiated) hyperspectral data of absorption and remote-sensing reflectance. The most useful spectral region for this discrimination extends generally from wavelengths of about 425-435 nm to wavelengths within the 495-540 nm range, although in the case of phytoplankton absorption data a broader spectral region can also provide satisfactory results.     

Remote chlorophyll-a retrieval in turbid, productive estuaries: Chesapeake Bay case study

Accurate remote assessment of phytoplankton chlorophyll a (chla) concentration is particularly challenging in turbid, productive waters. Recently a conceptual model containing reflectance in three spectral bands in the red and near infra-red range of the spectrum was suggested for retrieving chla concentrations in turbid productive waters; it was calibrated and validated in lakes and reservoirs in Nebraska and Iowa. The objective of this paper is to evaluate the performance of this three band model as well as its special case, the two-band model to estimate chla concentration in Chesapeake Bay, as representative of estuarine Case II waters, and to assess the accuracy of chla retrieval. To evaluate the model performance, dual spectroradiometers were used to measure subsurface spectral radiance reflectance in the visible and near infra-red range of the spectrum. Water samples were collected concurrently and contained widely variable chla (9 to 77.4 mg/m³) and total suspended solids (7-65 mg/L dry wt). Colored dissolved organic matter (CDOM) absorption at 440 nm was 0.20 to 2.50 m^− 1; Secchi disk transparency ranged from 0.28 to 1.5 m. The two- and three-band models were spectrally tuned to select the spectral bands for most accurate chla estimation. Strong linear relationships were established between analytically measured chla and both the three-band model [R^− 1(675)-R^− 1(695)] × R(730) and the two-band model R(720)/R(670), where R(λ) is reflectance at wavelength λ. The three-band model accounted for 81% of variation in chla and allowed estimation of chla with a root mean square error (RMSE) of less than 7.9 mg/m³, whereas the two-band model accounted for 79% of chla variability and RMSE of chla estimation was below 8.4 mg/m³. The three-band model with MERIS spectral bands allows accurate chla estimation with RMSE below 9.1 mg/m³. Two-band model with SeaWiFS bands and MODIS 667 nm and 748 nm bands can estimate chla with RMSE below 11 mg/m³. The findings underlined the rationale behind the conceptual model and demonstrated the robustness of this algorithm for chla retrieval in turbid, productive estuarine waters.     

土壤重金属Cu含量遥感反演的波段选择与最佳光谱分辨率研究

高光谱数据以其高光谱分辨率和多而连续的光谱波段为预测土壤重金属污染提供了有力工具,但波段选择方法与光谱分辨率的影响不容忽视。利用实验室测定的181个土壤光谱样本数据,利用逐步回归法进行土壤Cu含量反演的波段选择,进而利用偏最小二乘方回归PLSR方法建模,分析了波段数对Cu含量反演的影响;此外,采用高斯响应函数重采样方法,探讨了光谱分辨率降低对反演精度的影响。实验表明,预测重金属元素Cu含量的最佳波段数为10个,模型可决系数R2=0.7523,拟合均方根误差RMSE=0.4699;预测Cu含量的最佳光谱采样间隔为32 nm,R2=0.7028,RMSE=0.5147。该结果可能为将来设计低廉实用的高光谱卫星传感器提供指标论证,为模拟卫星传感器波段预测土壤重金属含量提供理论依据。     

Within-day variability of particulate organic carbon and remote-sensing reflectance during a bloom of Phaeocystis antarctica in the Ross Sea,Antarctica

We examined the within-day variability in seawater optical properties and biogeochemical constituents for a high-latitude location in the Ross Sea, Antarctica, during development of the annual spring phytoplankton bloom. Measurements of particulate organic carbon concentration (POC), chlorophyll-a concentration (Chl), and particle size distribution were conducted at 4–6 hour intervals in parallel with determinations of the spectral absorption and attenuation coefficients of particles, and the spectral remote-sensing reflectance of the surface ocean (R_rs). Surface POC and Chl exhibited more than a twofold variation throughout the day in the continuous presence of natural light. A minimum occurred near local noon coinciding with peak solar irradiance, a maximum in the evening, and a subsequent decrease throughout the night-time hours. These patterns were accompanied by large changes in the magnitude and spectral shape of R_rs, including the blue-to-green spectral band ratios used in ocean colour algorithms for estimating POC and Chl. The variability in R_rs could not be explained by changes in solar zenith angle, but was consistent with observations of within-day variations in spectral absorption and scattering by particles which were influenced by changes in the particle concentration and size distribution. The accuracy of an empirical ocean colour algorithm for estimating POC from R_rs was unaffected by within-day variability, implying that short-term variations in surface POC can be potentially monitored by multiple within-day measurements of R_rs, through means of in situ and remote sensing observations if available. Our findings also suggest that within-day changes in POC can be significant compared with the variability observed on meso-scale spatial scales, potentially confounding the interpretation of remote-sensing data obtained from temporal and spatial compositing of images measured at different times within a single day.     

A New Algorithm for Discussing Gröbner Bases with Parameters

Let F be a set of polynomials in the variables __x = x₁, . . . , x_nwith coefficients in R [__ a ], where R is a UFD and __ a = a₁, . . . ,a_m a set of parameters. In this paper we present a new algorithm for discussing Gröbner bases with parameters. The algorithm obtains all the cases over the parameters leading to different reduced Gröbner basis, when the parameters in F are substituted in an extension field K of R. This new algorithm improves Weispfenning’s comprehensive Gröbner basis CGB algorithm, obtaining a reduced complete set of compatible and disjoint cases. A final improvement determines the minimal singular variety outside of which the Gröbner basis of the generic case specializes properly. These constructive methods provide a very satisfactory discussion and rich geometrical interpretation in the applications.     

A simple semi-analytical model for remote estimation of chlorophyll-a in turbid waters: Validation

Accurate assessment of phytoplankton chlorophyll-a (chla) concentrations in turbid waters by means of remote sensing is challenging due to the optical complexity of case 2 waters. We have applied a recently developed model of the form [R_rs^? 1(λ₁) ? R_rs^? 1(λ₂)] × R_rs(λ₃) where R_rs(λ_i) is the remote-sensing reflectance at the wavelength λ_i, for the estimation of chla concentrations in turbid waters. The objectives of this paper are (a) to validate the three-band model as well as its special case, the two-band model R_rs^? 1(λ₁) × R_rs(λ₃), using datasets collected over a considerable range of optical properties, trophic status, and geographical locations in turbid lakes, reservoirs, estuaries, and coastal waters, and (b) to evaluate the extent to which the three-band model could be applied to the Medium Resolution Imaging Spectrometer (MERIS) and two-band model could be applied to the Moderate Resolution Imaging Spectroradiometer (MODIS) to estimate chla in turbid waters.The three-band model was calibrated and validated using three MERIS spectral bands (660–670 nm, 703.75–713.75 nm, and 750?757.5 nm), and the 2-band model was tested using two MODIS spectral bands (λ₁ = 662–672, λ₃ = 743–753 nm). We assessed the accuracy of chla prediction in four independent datasets without re-parameterization (adjustment of the coefficients) after initial calibration elsewhere. Although the validation data set contained widely variable chla (1.2 to 236 mg m^? 3), Secchi disk depth (0.18 to 4.1 m), and turbidity (1.3 to 78 NTU), chla predicted by the three-band algorithm was strongly correlated with observed chla (r² > 0.96), with a precision of 32% and average bias across data sets of ? 4.9% to 11%. Chla predicted by the two-band algorithm was also closely correlated with observed chla (r² > 0.92); however, the precision declined to 57%, and average bias across the data sets was 18% to 50.3%. These findings imply that, provided that an atmospheric correction scheme for the red and NIR bands is available, the extensive database of MERIS and MODIS imagery could be used for quantitative monitoring of chla in turbid waters.     

Sentences over Integral Domains and Their Computational Complexities

LetRbe a Hilbertian domain and letKbe its fraction field. Letψ(x₁, …, x_n, y) be a quantifier free arithmetical formula overR. We may also takeψ(x₁, …, x_n, y) to be an arithmetical formula overK[x₁, …, x_n] and write it asψ(y). In this paper we show that ifRhas enough non-units and x₁…x_n y ψ(x₁, …, x_n, y), called an ⁿ  sentence, is true inR, then y ψ(y) is true inK[x₁, …, x_n]. Also, ifR=K[T], whereKis an infinite integral domain andx₁…x_n y ψ(x₁, …, x_n, y)is true inR, then y ψ(y) is true inR[x₁, …, x_n]. These results are applied to find the upper and lower bounds of the time complexities of various decision problems on diophantine equations with parameters and arithmetical sentences. Some of the results are: 1. The decision problem of sentences and diophantine equations with parameters over the ring of integers of a global field are co-NP-complete. 2. The decision problem of sentences over the ring of integers of a global field is NP-complete. 3. LetKbe an infinite domain, the time complexities of the decision problems of equations with parameters and sentences over the polynomial ringK[t] are polynomial time reducible to factoring polynomials overK. 4. The decision problem of sentences over all algebraic integer rings is in P. 5. The decision problem of sentences over all integral domains with characteristic 0 is in P. 6. The time complexity of the decision problem of sentences over all integral domains is polynomial time reducible to factoring integers overZand factoring polynomials over finite fields.     

Bio-optical properties in waters influenced by the Mississippi River during low flow conditions

Spatial and temporal patterns of bio-optical properties were studied in the Northern Gulf of Mexico during cruises in April and October of 2000, a year during which the discharge volume from the Mississippi River was unusually low. Highly variable surface Chl a concentrations (0.1 to 17 mg m⁻³) and colored dissolved organic matter (CDOM) absorption (0.07 to 1.1 m⁻¹ at 412 nm) were observed in the study region that generally decreased with increasing salinity waters, being highest nearshore and decreasing at offshore stations. The optical properties of absorption, scattering, and diffuse attenuation coefficients reflected these distributions with phytoplankton particles and CDOM contributing to most of the spatial, vertical, and seasonal variability. The diffuse attenuation coefficient K_d(λ) and spectral remote sensing reflectance R_rs(λ) were linear functions of absorption and backscattering coefficients a(λ) and b_b(λ) through the downward average cosine μ_d and the ratio of variables f/Q at the SeaWiFS wavebands for waters with widely varying bio-optical conditions. Although various R_rs(λ) ratio combinations showed high correlation with surface Chl a concentrations and CDOM absorption at 412 nm, power law equations derived using the R_rs(490)/R_rs(555) and R_rs(510)/R_rs(555) ratios provided the best retrievals of Chl a concentrations and CDOM absorption from SeaWiFS reflectance data.     

Wavelet-based detection of crop zinc stress assessment using hyperspectral reflectance

Accurate detection of heavy metal-induced stress on the growth of crops is essential for agricultural ecological environment and food security. This study focuses on exploring singularity parameters as indicators for a crop's Zn stress level assessment by applying wavelet analysis to the hyperspectral reflectance. The field in which the experiment was conducted is located in the Changchun City, Jilin Province, China. The hyperspectral and biochemistry data from four crops growing in Zn contaminated soils: rice, maize, soybean and cabbage were collected. We performed a wavelet transform to the hyperspectral reflectance (350-1300 nm), and explored three categories of singularity parameters as indicators of crop Zn stress, including singularity range (S_R), singularity amplitude (S_A) and a Lipschitz exponent (α). The results indicated that (i) the wavelet coefficient of the fifth decomposition level by applying Daubechies 5 (db5) mother wavelets proved successful for identifying crop Zn stress; the S_R of crop concentrated on the region was around 550-850 nm of the spectral signal under Zn stress; (ii) the S_R stabilized, but S_A and α had developed some variations at the growth stages of the crop; (iii) the S_R, S_A and α were found among four crop species differentially; and moreover the S_A increased in relation to an increase in the S_R of crop species; (iv) the α had a strong non-linear relationship with the Zn concentration (R²:0.7601-0.9451); the S_A had a strong linear relationship with Zn concentration (R²:0.5141-0.8281). Singularity parameters can be used as indicators for a crop's Zn stress level as well as offer a quantitative analysis of the singularity of spectrum signal. The wavelet transform technique has been shown to be very promising in detecting crops with heavy metal stress.     

Assessing structural effects on PRI for stress detection in conifer forests

The retrieval of indicators of vegetation stress from remote sensing imagery is an important issue for the accurate assessment of forest decline. The Photochemical Reflectance Index (PRI) has been demonstrated as a physiological index sensitive to the epoxidation state of the xanthophyll cycle pigments and to photosynthetic efficiency, serving as a proxy for short-term changes in photosynthetic activity, stress condition, and pigment absorption, but highly affected by illumination conditions, viewing geometry and canopy structure. In this study, a diurnal airborne campaign was conducted over Pinus sylvestris and Pinus nigra forest areas with the Airborne Hyperspectral Scanner (AHS) to evaluate the effects of canopy structure on PRI when used as an indicator of stress in a conifer forest. The AHS airborne sensor was flown at two times (8:00 GMT and 12:00 GMT) over forest areas under varying field-measured stress levels, acquiring 2 m spatial resolution imagery in 80 spectral bands in the 0.43-12.5 μm spectral range. Five formulations of PRI (based on R₅₃₁ as a xanthophyll-sensitive spectral band) were calculated using different reference wavelengths, such as PRI₅₇₀ (reference band R_REF = R₅₇₀), and the PRI modifications PRI_m1 (R_REF = R₅₁₂), PRI_m2 (R_REF = R₆₀₀), PRI_m3 (R_REF = R₆₇₀), and PRI_m4 (R_REF = R₅₇₀, R₆₇₀), along with other structural indices such as NDVI, SR, OSAVI, MSAVI and MTVI2. In addition, thermal bands were used for the retrieval of the land surface temperature. A radiative transfer modeling method was conducted using the LIBERTY and INFORM models to assess the structural effects on the PRI formulations proposed, studying the sensitivity of PRI_m indices to detect stress levels while minimizing the effects caused by the conifer architecture. The PRI indices were related to stomatal conductance, xanthophyll epoxidation state (EPS) and crown temperature. The modeling analysis showed that the coefficient of variation (CV) for PRI was 50%, whereas the CV for PRIm1 (band R512 as a reference) was only 20%. Simulation and experimental results demonstrated that PRI_m1 (R_REF = R₅₁₂) was less sensitive than PRI (R_REF = R₅₇₀) to changes in Leaf Area Index (LAI) and tree densities. PRI₅₁₂ was demonstrated to be sensitive to EPS at both leaf (r² = 0.59) and canopy level (r² = 0.40), yielding superior performance than PRI₅₇₀ (r² = 0.21) at the canopy level. In addition, PRI₅₁₂ was significantly related to water stress indicators such as stomatal conductance (Gs; r² = 0.45) and water potential (Ψ; r² = 0.48), yielding better results than PRI₅₇₀ (Gs, r² = 0.21; Ψ, r² = 0.21) due to the structural effects found on the PRI₅₇₀ index at the canopy level.     

Leaf chlorophyll content retrieval from airborne hyperspectral remote sensing imagery

Hyperspectral remote sensing has great potential for accurate retrieval of forest biochemical parameters. In this paper, a hyperspectral remote sensing algorithm is developed to retrieve total leaf chlorophyll content for both open spruce and closed forests, and tested for open forest canopies. Ten black spruce (Picea mariana (Mill.)) stands near Sudbury, Ontario, Canada, were selected as study sites, where extensive field and laboratory measurements were carried out to collect forest structural parameters, needle and forest background optical properties, and needle biophysical parameters and biochemical contents chlorophyll a and b. Airborne hyperspectral remote sensing imagery was acquired, within one week of ground measurements, by the Compact Airborne Spectrographic Imager (CASI) in a hyperspectral mode, with 72 bands and half bandwidth 4.25-4.36 nm in the visible and near-infrared region and a 2 m spatial resolution. The geometrical-optical model 4-Scale and the modified leaf optical model PROSPECT were combined to estimate leaf chlorophyll content from the CASI imagery. Forest canopy reflectance was first estimated with the measured leaf reflectance and transmittance spectra, forest background reflectance, CASI acquisition parameters, and a set of stand parameters as inputs to 4-Scale. The estimated canopy reflectance agrees well with the CASI measured reflectance in the chlorophyll absorption sensitive regions, with discrepancies of 0.06%-1.07% and 0.36%-1.63%, respectively, in the average reflectances of the red and red-edge region. A look-up-table approach was developed to provide the probabilities of viewing the sunlit foliage and background, and to determine a spectral multiple scattering factor as functions of leaf area index, view zenith angle, and solar zenith angle. With the look-up tables, the 4-Scale model was inverted to estimate leaf reflectance spectra from hyperspectral remote sensing imagery. Good agreements were obtained between the inverted and measured leaf reflectance spectra across the visible and near-infrared region, with R² = 0.89 to R² = 0.97 and discrepancies of 0.02%-3.63% and 0.24%-7.88% in the average red and red-edge reflectances, respectively. Leaf chlorophyll content was estimated from the retrieved leaf reflectance spectra using the modified PROSPECT inversion model, with R² = 0.47, RMSE = 4.34 μg/cm², and jackknifed RMSE of 5.69 μg/cm² for needle chlorophyll content ranging from 24.9 μg/cm² to 37.6 μg/cm². The estimates were also assessed at leaf and canopy scales using chlorophyll spectral indices TCARI/OSAVI and MTCI. An empirical relationship of simple ratio derived from the CASI imagery to the ground-measured leaf area index was developed (R² = 0.88) to map leaf area index. Canopy chlorophyll content per unit ground surface area was then estimated, based on the spatial distributions of leaf chlorophyll content per unit leaf area and the leaf area index.     

Potential signatures of heavy metal complexes in lichen reflectance spectra

Lichens are sensitive to atmospheric pollutants emitted from anthropogenic activities and are thus effective biomonitors. A variety of heavy metals, such as nickel (Ni), iron (Fe), lead (Pb), copper (Cu), and cadmium (Cd), can be emitted by metal smelters. The purpose of this study was twofold: (1) to measure the spectral reflectance properties (350–2500 nm) of expected heavy metal complexes in lichens (oxalates and sulphides); and (2) to determine whether these complexes contribute features to reflectance spectra of lichens from the vicinity of a heavy metal smelter. Some metal oxalate spectra are characterized by crystal field transition absorption bands in the 500–1300 nm region, which are specific to the particular metal cation they contain and its oxidation state. The 1900–2500 nm region exhibits multiple absorption bands attributable to the oxalate molecule. The metal sulphide reflectance spectra are characterized by generally low reflectance and few if any strong or diagnostic spectral features; those that are found can be related to a specific cation and its oxidation state. These spectra were used to determine whether reflectance spectra of a diverse suite of lichens collected downwind of a smelter showed spectral evidence indicative of heavy metal oxalates or sulphides. The lichen spectra, coupled with the oxalate and sulphide spectra and independently determined heavy metal concentration, failed to reveal spectral features that could be unambiguously related to heavy metal complexes. This was likely due to a number of causes: lichen reflectance spectra have absorption bands that overlap those of oxalates; oxalate and sulphide concentrations may have been too low to allow for their unambiguous identification, and lichen spectra are naturally diverse in the region below 1300 nm. There were no strong or significant linear trends between metal concentrations and distance from the smelter (coefficient of determination (R²) values <0.05), or between absorption band depths in the lichen spectra and distance from the smelter (R² values <0.06). This was likely due to the inclusion of multiple lichen species in the analysis, which may interact with airborne pollutants in different ways, and microenvironmental effects.     

Evaluating the severity level of cotton Verticillium using spectral signature analysis

High spatial or spectral resolution remote sensing might be an efficient method for estimating Verticillium wilt incidence in cotton. The objectives of this study were to characterize leaf spectra and the physiological and biochemical parameters of cotton (Gossypium hirsutum) damaged by Verticillium dahliae Kleb. (simply, Verticillium) to determine the wavelengths of those leaves that were most responsive to cotton with Verticillium and to develop a spectral model to predict the severity levels (SLs) of Verticillium through evaluation of the SLs of cotton leaves with Verticillium at different growth stages using reflectance and the first derivative (FD) spectrum. The study revealed that the values of the physiological and biochemical parameters all gradually decreased with increasing SLs in cotton leaves infected with Verticillium. The spectral characteristics of cotton leaves infected with Verticillium were significant compared to healthy ones. The reflectance of cotton leaves increased with increasing SLs of SLs disease in the range of 400–2500 nm (excluding 700–900 nm). The values of FD spectrum changed significantly at the red edge of the chlorophyll absorption feature (680–740 nm). The wavelength position of the red edge shifted towards shorter wavelengths and the red-edge swing decreased with respect to increasing SLs. From this study, the raw spectral bands of 437–724 and 909–2500 nm and the FD spectra bands of 535–603 and 699–750 nm can be selected as sensitive bands for estimating the SLs of disease in cotton leaves. Inversion models have been established to estimate the SLs of cotton leaves infected with Verticillium. Of all models, the model of R _700nm/R _825nm was superior for quantitatively estimating the disease SLs of cotton leaves infected with Verticillium in practice: its root mean square error (RMSE) was 0.866 and relative error (RE) was only 0.012. Thus, both the selected wavelength ranges and the chosen reflectance models were good indicators of damage caused by Verticillium to cotton leaves. The results provide theoretical support for large-scale monitoring of cotton infected with Verticillium by air- and spaceborne remote sensing.     

Mason: morphological simplification

The traditional rounding and filleting morphological filters are biased. Hence, as r grows, the rounding R_r (S) of S shrinks and the filleting F_r (S) grows. A shape S is r-regular when R_r (S) = F_r (S) = S. The combinations F_r (R_r (S)) and R_r (F_r (S)) produce nearly r-regular shapes, but retain a bias: F_r (R_r (S)) is usually smaller than S and R_r (F_r (S)) is larger. To overcome this bias, we propose a new filter, called Mason. The r-mortar M_r (S) of S is F_r (S)–R_r (S), and the stability of a point P with respect to S is the smallest value of r for which P belongs to M_r (S). Stability provides important information about the shape’s imbedding that cannot be obtained through traditional topological or differential analysis tools. F_r (R_r (S)) and R_r (F_r (S)) only affect space in M_r (S). For each maximally connected component of M_r (S), Mason performs either F_r (R_r (S)) or R_r (F_r (S)), choosing the combination that alters the smallest portion of that component. Hence, Mason acts symmetrically on the shape and on its complement. Its output is guaranteed to have a smaller symmetric difference with the original shape than that of either combination F_r (R_r (S)) or R_r (F_r (S)). Many previously proposed shape simplification algorithms were focused on reducing the combinatorial storage or processing costs of a shape at the expense of the smoothness and regularity or altered the shape in regular portions that did not exhibit any high frequency complexity. Mason is the first shape simplification operator that is independent of the particular representation and offers the advantage of preserving portions of the boundary of S that are regular at the desired scale.     

Bio-optical algorithm evaluation for MODIS for western Canada coastal waters: An exploratory approach using in situ reflectance

Biophysical and above-water reflectance measurements collected in 2006 were used to evaluate the OC3M, standard GSM01, and a modified version of the GSM01 algorithms for estimating chlorophyll-a (chl) concentrations in the Strait of Georgia, located off the southwest coast of Canada. The Strait was generally a case 2 water body, transitioning from chromophoric dissolved organic matter (CDOM) dominant in the central region to possibly particulate dominant in Fraser River plume regions. Results showed that the OC3M algorithm was somewhat effective (R² = 0.550) outside the most turbid areas of the Fraser River plume. However, a systematic overestimation of lower chl concentrations was found, which may have been related to the higher CDOM absorption observed throughout the Strait. The standard GSM01 algorithm had moderately good agreement with measured CDOM absorption (R² = 0.593) and total suspended solids (TSS) concentrations (R² = 0.888), but was ineffective at estimating chl concentrations. Localized characterization of the CDOM absorption, through a hyperbolic CDOM model, improved the modified GSM01 results with slightly better agreement with measure CDOM absorption (R² = 0.614) and TSS concentrations (R² = 0.933). When the modified GSM01 algorithm was limited to regions with lower combined CDOM and non-algal particulate absorption (a_dg (443) < 0.7 m^− 1), it was more effective then the OC3M algorithm at estimating chl concentrations. This suggests that a threshold value on the a_dg (443) or b_bp (443) estimated by the GSM01 algorithm may be beneficial for limiting turbidity influence on the algorithm. The further reinterpretation of phytoplankton absorption from the modified GSM01 algorithm with a two-component phytoplankton model resulted in a chl relationship with an R² = 0.677 and a linear slope closer to one.     

A new metric based on extended spatial frequency and its application to DWT based fusion algorithms

A new quantitative metric is proposed to objectively evaluate the quality of fused imagery. The measured value of the proposed metric is used as feedback to a fusion algorithm such that the image quality of the fused image can potentially be improved. This new metric, called the ratio of spatial frequency error (rSFe), is derived from the definition of a previous measure termed “spatial frequency” (SF) that reflects local intensity variation. In this work, (1) the concept of SF is first extended by adding two diagonal SFs, then, (2) a reference SF (SF_R) is computed from the input images, and finally, (3) the error SF (SF_E) (subtracting the fusion SF from the reference SF), or the ratio of SF error (rSFe = SF_E/SF_R), is used as a fusion quality metric. The rSFe (which can be positive or negative) indicates the direction of fusion error—over-fused (if rSFe > 0) or under-fused (if rSFe < 0). Thus, the rSFe value can be back propagated to the fusion algorithm (BP fusion), thereby directing further parameter adjustments in order to achieve a better-fused image. The accuracy of the rSFe is verified with other quantitative measurements such as the root mean square error (RMSE) and the image quality index (IQI), as well as with a qualitative perceptual evaluation based on a standard psychophysical paradigm. An advanced wavelet transform (aDWT) method that incorporates principal component analysis (PCA) and morphological processing into a regular DWT fusion algorithm is implemented with two adjustable parameters—the number of levels of DWT decompositions and the length of the selected wavelet. Results with aDWT were compared to those with a regular DWT and with a Laplacian pyramid. After analyzing several inhomogeneous image groups, experimental results showed that the proposed metric, rSFe, is consistent with RMSE and IQI, and is especially powerful and efficient for realizing the iterative BP fusion in order to achieve a better image quality. Human perceptual assessment was measured and found to strongly support the assertion that the aDWT offers a significant improvement over the DWT and pyramid methods.     

Modelling heat,water and carbon fluxes in mown grassland under multi-objective and multi-criteria constraints

A Monte Carlo-based calibration and uncertainty assessment was performed for heat, water and carbon (C) fluxes, simulated by a soil-plant-atmosphere system model (CoupModel), in mown grassland. Impact of different multi-objective and multi-criteria constraints was investigated on model performance and parameter behaviour. Good agreements between hourly modelled and measurement data were obtained for latent and sensible heat fluxes (R² = 0.61, ME = 0.48 MJ m⁻² day⁻¹), soil water contents (R² = 0.68, ME = 0.34%) and carbon-dioxide flux (R² = 0.60, ME = −0.18 g C m⁻² day⁻¹). Multi-objective and multi-criteria constraints were efficient in parameter conditioning, reducing simulation uncertainty and identifying critical parameters. Enforcing multi-constraints separately on heat, water and C processes resulted in the highest model improvement for that specific process, including some improvement too for other processes. Imposing multi-constraints on all groups of variables, associated with heat, water and C fluxes together, resulted in general effective parameters conditioning and model improvement.