A New Phase Field Model of a `Gas of Circles' for Tree Crown Extraction from Aerial Images

We describe a model for tree crown extraction from aerial images, a problem of great practical importance for the forestry industry. The novelty lies in the prior model of the region occupied by tree crowns in the image, which is a phase field version of the higher-order active contour inflection point 'gas of circles' model. The model combines the strengths of the inflection point model with those of the phase field framework: it removes the 'phantom circles' produced by the original 'gas of circles' model, while executing two orders of magnitude faster than the contour-based inflection point model. The model has many other areas of application e.g., to imagery in nanotechnology, biology, and physics

A multi-layer phase field model for extracting multiple near-circular objects

This paper proposes a functional that assigns low `energy' to sets of subsets of the image domain consisting of a number of possibly overlapping near-circular regions of approximately a given radius: a `gas of circles'. The model can be used as a prior for object extraction whenever the objects conform to the `gas of circles' geometry, e.g. cells in biological images. Configurations are represented by a multi-layer phase field. Each layer has an associated function, regions being defined by thresholding. Intra-layer interactions assign low energy to configurations consisting of non-overlapping near-circular regions, while overlapping regions are represented in separate layers. Inter-layer interactions penalize overlaps. Here we present a theoretical and experimental analysis of the model

A multi-layer `gas of circles' Markov random field model for the extraction of overlapping near-circular objects

We propose a multi-layer binary Markov random field (MRF) model that assigns high probability to object configurations in the image domain consisting of an unknown number of possibly touching or overlapping near-circular objects of approximately a given size. Each layer has an associated binary field that specifies a region corresponding to objects. Overlapping objects are represented by regions in different layers. Within each layer, long-range interactions favor connected components of approximately circular shape, while regions in different layers that overlap are penalized. Used as a prior coupled with a suitable data likelihood, the model can be used for object extraction from images, e.g. cells in biological images or densely-packed tree crowns in remote sensing images. We present a theoretical and experimental analysis of the model, and demonstrate its performance on various synthetic and biomedical images

A multi-layer 'gas of circles' Markov random field model for the extraction of overlapping near-circular objects.

We propose a multi-layer binary Markov random field (MRF) model that assigns high probability to object configurations in the image domain consisting of an unknown number of possibly touching or overlapping near-circular objects of approximately a given size. Each layer has an associated binary field that specifies a region corresponding to objects. Overlapping objects are represented by regions in different layers. Within each layer, long-range interactions favor connected components of approximately circular shape, while regions in different layers that overlap are penalized. Used as a prior coupled with a suitable data likelihood, the model can be used for object extraction from images, e.g. cells in biological images or densely-packed tree crowns in remote sensing images. We present a theoretical and experimental analysis of the model, and demonstrate its performance on various synthetic and biomedical images

Quantifying the urban forest environment using dense discrete return LiDAR and aerial color imagery for segmentation and object-level biomass assessment

The urban forest is becoming increasingly important in the contexts of urban green space and recreation, carbon sequestration and emission offsets, and socio-economic impacts. In addition to aesthetic value, these green spaces remove airborne pollutants, preserve natural resources, and mitigate adverse climate changes, among other benefits. A great deal of attention recently has been paid to urban forest management. However, the comprehensive monitoring of urban vegetation for carbon sequestration and storage is an under-explored research area. Such an assessment of carbon stores often requires information at the individual tree level, necessitating the proper masking of vegetation from the built environment, as well as delineation of individual tree crowns. As an alternative to expensive and time-consuming manual surveys, remote sensing can be used effectively in characterizing the urban vegetation and man-made objects. Many studies in this field have made use of aerial and multispectral/hyperspectral imagery over cities. The emergence of light detection and ranging (LiDAR) technology, however, has provided new impetus to the effort of extracting objects and characterizing their 3D attributes - LiDAR has been used successfully to model buildings and urban trees. However, challenges remain when using such structural information only, and researchers have investigated the use of fusion-based approaches that combine LiDAR and aerial imagery to extract objects, thereby allowing the complementary characteristics of the two modalities to be utilized. In this study, a fusion-based classification method was implemented between high spatial resolution aerial color (RGB) imagery and co-registered LiDAR point clouds to classify urban vegetation and buildings from other urban classes/cover types. Structural, as well as spectral features, were used in the classification method. These features included height, flatness, and the distribution of normal surface vectors from LiDAR data, along with a non-calibrated LiDAR-based vegetation index, derived from combining LiDAR intensity at 1064 nm with the red channel of the RGB imagery. This novel index was dubbed the LiDAR-infused difference vegetation index (LDVI). Classification results indicated good separation between buildings and vegetation, with an overall accuracy of 92% and a kappa statistic of 0.85. A multi-tiered delineation algorithm subsequently was developed to extract individual tree crowns from the identified tree clusters, followed by the application of species-independent biomass models based on LiDAR-derived tree attributes in regression analysis. These LiDAR-based biomass assessments were conducted for individual trees, as well as for clusters of trees, in cases where proper delineation of individual trees was impossible. The detection accuracy of the tree delineation algorithm was 70%. The LiDAR-derived biomass estimates were validated against allometry-based biomass estimates that were computed from field-measured tree data. It was found out that LiDAR-derived tree volume, area, and different distribution parameters of height (e.g., maximum height, mean of height) are important to model biomass. The best biomass model for the tree clusters and the individual trees showed an adjusted R-Squared value of 0.93 and 0.58, respectively. The results of this study showed that the developed fusion-based classification approach using LiDAR and aerial color (RGB) imagery is capable of producing good object detection accuracy. It was concluded that the LDVI can be used in vegetation detection and can act as a substitute for the normalized difference vegetation index (NDVI), when near-infrared multiband imagery is not available. Furthermore, the utility of LiDAR for characterizing the urban forest and associated biomass was proven. This work could have significant impact on the rapid and accurate assessment of urban green spaces and associated carbon monitoring and management

Comparing accuracy of airborne laser scanning and TerraSAR-X radar images in the estimation of plot-level forest variables

Peer reviewe

Extraction of Unfoliaged Trees from Terrestrial Image Sequences

This thesis presents a generative statistical approach for the fully automatic three-dimensional (3D) extraction and reconstruction of unfoliaged deciduous trees from wide-baseline image sequences. Tree models improve the realism of 3D Geoinformation systems (GIS) by adding a natural touch. Unfoliaged trees are, however, difficult to reconstruct from images due to partially weak contrast, background clutter, occlusions, and particularly the possibly varying order of branches in images from different viewpoints. The proposed approach combines generative modeling by L-systems and statistical maximum a posteriori (MAP) estimation for the extraction of the 3D branching structure of trees. Background estimation is conducted by means of mathematical (gray scale) morphology as basis for generative modeling. A Gaussian likelihood function based on intensity differences is employed to evaluate the hypotheses. A mechanism has been devised to control the sampling sequence of multiple parameters in the Markov Chain considering their characteristics and the performance in the previous step. A tree is classified into three typical branching types after the extraction of the first level of branches and more specific Production Rules of L-systems are used accordingly. Generic prior distributions for parameters are refined based on already extracted branches in a Bayesian framework and integrated into the MAP estimation. By these means most of the branching structure besides tiny twigs can be reconstructed. Results are presented in the form of VRML (Virtual Reality Modeling Language) models demonstrating the potential of the approach as well as its current shortcomings.Diese Dissertationsschrift stellt einen generativen statistischen Ansatz für die vollautomatische drei-dimensionale (3D) Extraktion und Rekonstruktion unbelaubter Laubbäume aus Bildsequenzen mit großer Basis vor. Modelle für Bäume verbessern den Realismus von 3D Geoinformationssystemen (GIS), indem sie Letzteren eine natürliche Note geben. Wegen z.T. schwachem Kontrast, Störobjekten im Hintergrund, Verdeckungen und insbesondere der möglicherweise unterschiedlichen Ordnung der Äste in Bildern von verschiedenen Blickpunkten sind unbelaubte Bäume aber schwierig zu rekonstruieren. Der vorliegende Ansatz kombiniert generative Modellierung mittels L-Systemen und statistische Maximum A Posteriori (MAP) Schätzung für die Extraktion der 3D Verzweigungsstruktur von Bäumen. Hintergrund-Schätzung wird auf Grundlage von mathematischer (Grauwert) Morphologie als Basis für die generative Modellierung durchgeführt. Für die Bewertung der Hypothesen wird eine Gaußsche Likelihood-Funktion basierend auf Intensitätsunterschieden benutzt. Es wurde ein Mechanismus entworfen, der die Reihenfolge der Verwendung mehrerer Parameter für die Markoff-Kette basierend auf deren Charakteristik und Performance im letzten Schritt kontrolliert. Ein Baum wird nach der Extraktion der ersten Stufe von Ästen in drei typische Verzweigungstypen klassifiziert und es werden entsprechend Produktionsregeln von spezifischen L-Systemen verwendet. Basierend auf bereits extrahierten Ästen werden generische Prior-Verteilungen für die Parameter in einem Bayes’schen Rahmen verfeinert und in die MAP Schätzung integriert. Damit kann ein großer Teil der Verzweigungsstruktur außer kleinen Ästen extrahiert werden. Die Ergebnisse werden als VRML (Virtual Reality Modeling Language) Modelle dargestellt. Sie zeigen das Potenzial aber auch die noch vorhandenen Defizite des Ansatzes

Developing Allometric Equations for Teak Plantations Located in the Coastal Region of Ecuador from Terrestrial Laser Scanning Data

Traditional studies aimed at developing allometric models to estimate dry above-ground biomass (AGB) and other tree-level variables, such as tree stem commercial volume (TSCV) or tree stem volume (TSV), usually involves cutting down the trees. Although this method has low uncertainty, it is quite costly and inefficient since it requires a very time-consuming field work. In order to assist in data collection and processing, remote sensing is allowing the application of non-destructive sampling methods such as that based on terrestrial laser scanning (TLS). In this work, TLS-derived point clouds were used to digitally reconstruct the tree stem of a set of teak trees (Tectona grandis Linn. F.) from 58 circular reference plots of 18 m radius belonging to three different plantations located in the Coastal Region of Ecuador. After manually selecting the appropriate trees from the entire sample, semi-automatic data processing was performed to provide measurements of TSCV and TSV, together with estimates of AGB values at tree level. These observed values were used to develop allometric models, based on diameter at breast height (DBH), total tree height (h), or the metric DBH2 × h, by applying a robust regression method to remove likely outliers. Results showed that the developed allometric models performed reasonably well, especially those based on the metric DBH2 × h, providing low bias estimates and relative RMSE values of 21.60% and 16.41% for TSCV and TSV, respectively. Allometric models only based on tree height were derived from replacing DBH by h in the expression DBH2 x h, according to adjusted expressions depending on DBH classes (ranges of DBH). This finding can facilitate the obtaining of variables such as AGB (carbon stock) and commercial volume of wood over teak plantations in the Coastal Region of Ecuador from only knowing the tree height, constituting a promising method to address large-scale teak plantations monitoring from the canopy height models derived from digital aerial stereophotogrammetry

Ecological impacts of deforestation and forest degradation in the peat swamp forests of northwestern Borneo

Tropical peatlands have some of the highest carbon densities of any ecosystem and are under enormous development pressure. This dissertation aimed to provide better estimates of the scales and trends of ecological impacts from tropical peatland deforestation and degradation across more than 7,000 hectares of both intact and disturbed peatlands in northwestern Borneo. We combined direct field sampling and airborne Light Detection And Ranging (LiDAR) data to empirically quantify forest structures and aboveground live biomass across a largely intact tropical peat dome. The observed biomass density of 217.7 ± 28.3 Mg C hectare-1 was very high, exceeding many other tropical rainforests. The canopy trees were ~65m in height, comprising 81% of the aboveground biomass. Stem density was observed to increase across the 4m elevational gradient from the dome margin to interior with decreasing stem height, crown area and crown roughness. We also developed and implemented a multi-temporal, Landsat resolution change detection algorithm for identify disturbance events and assessing forest trends in aseasonal tropical peatlands. The final map product achieved more than 92% user’s and producer’s accuracy, revealing that after more than 25 years of management and disturbances, only 40% of the area was intact forest. Using a chronosequence approach, with a space for time substitution, we then examined the temporal dynamics of peatlands and their recovery from disturbance. We observed widespread arrested succession in previously logged peatlands consistent with hydrological limits on regeneration and degraded peat quality following canopy removal. We showed that clear-cutting, selective logging and drainage could lead to different modes of regeneration and found that statistics of the Enhanced Vegetation Index and LiDAR height metrics could serve as indicators of harvesting intensity, impacts, and regeneration stage. Long-term, continuous monitoring of the hydrology and ecology of peatland can provide key insights regarding best management practices, restoration, and conservation priorities for this unique and rapidly disappearing ecosystem

Biomass Representation in Synthetic Aperture Radar Interferometry Data Sets

This work makes an attempt to explain the origin, features and potential applications of the elevation bias of the synthetic aperture radar interferometry (InSAR) datasets over areas covered by vegetation. The rapid development of radar-based remote sensing methods, such as synthetic aperture radar (SAR) and InSAR, has provided an alternative to the photogrammetry and LiDAR for determining the third dimension of topographic surfaces. The InSAR method has proved to be so effective and productive that it allowed, within eleven days of the space shuttle mission, for acquisition of data to develop a three-dimensional model of almost the entire land surface of our planet. This mission is known as the Shuttle Radar Topography Mission (SRTM). Scientists across the geosciences were able to access the great benefits of uniformity, high resolution and the most precise digital elevation model (DEM) of the Earth like never before for their a wide variety of scientific and practical inquiries. Unfortunately, InSAR elevations misrepresent the surface of the Earth in places where there is substantial vegetation cover. This is a systematic error of unknown, yet limited (by the vertical extension of vegetation) magnitude. Up to now, only a limited number of attempts to model this error source have been made. However, none offer a robust remedy, but rather partial or case-based solutions. More work in this area of research is needed as the number of airborne and space-based InSAR elevation models has been steadily increasing over the last few years, despite strong competition from LiDAR and optical methods. From another perspective, however, this elevation bias, termed here as the “biomass impenetrability”, creates a great opportunity to learn about the biomass. This may be achieved due to the fact that the impenetrability can be considered a collective response to a few factors originating in 3D space that encompass the outermost boundaries of vegetation. The biomass, presence in InSAR datasets or simply the biomass impenetrability, is the focus of this research. The report, presented in a sequence of sections, gradually introduces terminology, physical and mathematical fundamentals commonly used in describing the propagation of electromagnetic waves, including the Maxwell equations. The synthetic aperture radar (SAR) and InSAR as active remote sensing methods are summarised. In subsequent steps, the major InSAR data sources and data acquisition systems, past and present, are outlined. Various examples of the InSAR datasets, including the SRTM C- and X-band elevation products and INTERMAP Inc. IFSAR digital terrain/surface models (DTM/DSM), representing diverse test sites in the world are used to demonstrate the presence and/or magnitude of the biomass impenetrability in the context of different types of vegetation – usually forest. Also, results of investigations carried out by selected researchers on the elevation bias in InSAR datasets and their attempts at mathematical modelling are reviewed. In recent years, a few researchers have suggested that the magnitude of the biomass impenetrability is linked to gaps in the vegetation cover. Based on these hints, a mathematical model of the tree and the forest has been developed. Three types of gaps were identified; gaps in the landscape-scale forest areas (Type 1), e.g. forest fire scares and logging areas; a gap between three trees forming a triangle (Type 2), e.g. depending on the shape of tree crowns; and gaps within a tree itself (Type 3). Experiments have demonstrated that Type 1 gaps follow the power-law density distribution function. One of the most useful features of the power-law distributed phenomena is their scale-independent property. This property was also used to model Type 3 gaps (within the tree crown) by assuming that these gaps follow the same distribution as the Type 1 gaps. A hypothesis was formulated regarding the penetration depth of the radar waves within the canopy. It claims that the depth of penetration is simply related to the quantisation level of the radar backscattered signal. A higher level of bits per pixels allows for capturing weaker signals arriving from the lower levels of the tree crown. Assuming certain generic and simplified shapes of tree crowns including cone, paraboloid, sphere and spherical cap, it was possible to model analytically Type 2 gaps. The Monte Carlo simulation method was used to investigate relationships between the impenetrability and various configurations of a modelled forest. One of the most important findings is that impenetrability is largely explainable by the gaps between trees. A much less important role is played by the penetrability into the crown cover. Another important finding is that the impenetrability strongly correlates with the vegetation density. Using this feature, a method for vegetation density mapping called the mean maximum impenetrability (MMI) method is proposed. Unlike the traditional methods of forest inventories, the MMI method allows for a much more realistic inventory of vegetation cover, because it is able to capture an in situ or current situation on the ground, but not for areas that are nominally classified as a “forest-to-be”. The MMI method also allows for the mapping of landscape variation in the forest or vegetation density, which is a novel and exciting feature of the new 3D remote sensing (3DRS) technique. Besides the inventory-type applications, the MMI method can be used as a forest change detection method. For maximum effectiveness of the MMI method, an object-based change detection approach is preferred. A minimum requirement for the MMI method is a time-lapsed reference dataset in the form, for example, of an existing forest map of the area of interest, or a vegetation density map prepared using InSAR datasets. Preliminary tests aimed at finding a degree of correlation between the impenetrability and other types of passive and active remote sensing data sources, including TerraSAR-X, NDVI and PALSAR, proved that the method most sensitive to vegetation density was the Japanese PALSAR - L-band SAR system. Unfortunately, PALSAR backscattered signals become very noisy for impenetrability below 15 m. This means that PALSAR has severe limitations for low loadings of the biomass per unit area. The proposed applications of the InSAR data will remain indispensable wherever cloud cover obscures the sky in a persistent manner, which makes suitable optical data acquisition extremely time-consuming or nearly impossible. A limitation of the MMI method is due to the fact that the impenetrability is calculated using a reference DTM, which must be available beforehand. In many countries around the world, appropriate quality DTMs are still unavailable. A possible solution to this obstacle is to use a DEM that was derived using P-band InSAR elevations or LiDAR. It must be noted, however, that in many cases, two InSAR datasets separated by time of the same area are sufficient for forest change detection or similar applications