Final report on research project PS2010, proof of concept of automated mapping of weeds in arable fields

Many weeds occur in patches but farmers frequently spray whole fields to control the weeds in these patches. Given a geo-referenced weed map, technology exists to confine spraying to these patches. Adoption of patch spraying by arable farmers has, however, been negligible partly due to the difficulty of constructing weed maps. Building on previous DEFRA and HGCA projects, this proposal aims to develop and evaluate a machine vision system to automate the weed mapping process. The project thereby addresses the principal technical stumbling block to widespread adoption of site specific weed management (SSWM). The accuracy of weed identification by machine vision based on a single field survey may be inadequate to create herbicide application maps. We therefore propose to test the hypothesis that sufficiently accurate weed maps can be constructed by integrating information from geo-referenced images captured automatically at different times of the year during normal field activities. Accuracy of identification will also be increased by utilising a priori knowledge of weeds present in fields. To prove this concept, images will be captured from arable fields on two farms and processed offline to identify and map the weeds, focussing especially on black-grass, wild oats, barren brome, couch grass and cleavers. As advocated by Lutman et al. (2002), the approach uncouples the weed mapping and treatment processes and builds on the observation that patches of these weeds are quite stable in arable fields. There are three main aspects to the project. 1) Machine vision hardware. Hardware component parts of the system are one or more cameras connected to a single board computer (Concurrent Solutions LLC) and interfaced with an accurate Global Positioning System (GPS) supplied by Patchwork Technology. The camera(s) will take separate measurements for each of the three primary colours of visible light (red, green and blue) in each pixel. The basic proof of concept can be achieved in principle using a single camera system, but in practice systems with more than one camera may need to be installed so that larger fractions of each field can be photographed. Hardware will be reviewed regularly during the project in response to feedback from other work packages and updated as required. 2) Image capture and weed identification software. The machine vision system will be attached to toolbars of farm machinery so that images can be collected during different field operations. Images will be captured at different ground speeds, in different directions and at different crop growth stages as well as in different crop backgrounds. Having captured geo-referenced images in the field, image analysis software will be developed to identify weed species by Murray State and Reading Universities with advice from The Arable Group. A wide range of pattern recognition and in particular Bayesian Networks will be used to advance the state of the art in machine vision-based weed identification and mapping. Weed identification algorithms used by others are inadequate for this project as we intend to collect and correlate images collected at different growth stages. Plants grown for this purpose by Herbiseed will be used in the first instance. In addition, our image capture and analysis system will include plant characteristics such as leaf shape, size, vein structure, colour and textural pattern, some of which are not detectable by other machine vision systems or are omitted by their algorithms. Using such a list of features observable using our machine vision system, we will determine those that can be used to distinguish weed species of interest. 3) Weed mapping. Geo-referenced maps of weeds in arable fields (Reading University and Syngenta) will be produced with advice from The Arable Group and Patchwork Technology. Natural infestations will be mapped in the fields but we will also introduce specimen plants in pots to facilitate more rigorous system evaluation and testing. Manual weed maps of the same fields will be generated by Reading University, Syngenta and Peter Lutman so that the accuracy of automated mapping can be assessed. The principal hypothesis and concept to be tested is that by combining maps from several surveys, a weed map with acceptable accuracy for endusers can be produced. If the concept is proved and can be commercialised, systems could be retrofitted at low cost onto existing farm machinery. The outputs of the weed mapping software would then link with the precision farming options already built into many commercial sprayers, allowing their use for targeted, site-specific herbicide applications. Immediate economic benefits would, therefore, arise directly from reducing herbicide costs. SSWM will also reduce the overall pesticide load on the crop and so may reduce pesticide residues in food and drinking water, and reduce adverse impacts of pesticides on non-target species and beneficials. Farmers may even choose to leave unsprayed some non-injurious, environmentally-beneficial, low density weed infestations. These benefits fit very well with the anticipated legislation emerging in the new EU Thematic Strategy for Pesticides which will encourage more targeted use of pesticides and greater uptake of Integrated Crop (Pest) Management approaches, and also with the requirements of the Water Framework Directive to reduce levels of pesticides in water bodies. The greater precision of weed management offered by SSWM is therefore a key element in preparing arable farming systems for the future, where policy makers and consumers want to minimise pesticide use and the carbon footprint of farming while maintaining food production and security. The mapping technology could also be used on organic farms to identify areas of fields needing mechanical weed control thereby reducing both carbon footprints and also damage to crops by, for example, spring tines. Objective i. To develop a prototype machine vision system for automated image capture during agricultural field operations; ii. To prove the concept that images captured by the machine vision system over a series of field operations can be processed to identify and geo-reference specific weeds in the field; iii. To generate weed maps from the geo-referenced, weed plants/patches identified in objective (ii).

Nonlinear model structure design and construction using orthogonal least squares and D-optimality design

A very efficient learning algorithm for model subset selection is introduced based on a new composite cost function that simultaneously optimizes the model approximation ability and model robustness and adequacy. The derived model parameters are estimated via forward orthogonal least squares, but the model subset selection cost function includes a D-optimality design criterion that maximizes the determinant of the design matrix of the subset to ensure the model robustness, adequacy, and parsimony of the final model. The proposed approach is based on the forward orthogonal least square (OLS) algorithm, such that new D-optimality-based cost function is constructed based on the orthogonalization process to gain computational advantages and hence to maintain the inherent advantage of computational efficiency associated with the conventional forward OLS approach. Illustrative examples are included to demonstrate the effectiveness of the new approach.

Neurofuzzy design and model construction of nonlinear dynamical processes from data

A common problem in many data based modelling algorithms such as associative memory networks is the problem of the curse of dimensionality. In this paper, a new two-stage neurofuzzy system design and construction algorithm (NeuDeC) for nonlinear dynamical processes is introduced to effectively tackle this problem. A new simple preprocessing method is initially derived and applied to reduce the rule base, followed by a fine model detection process based on the reduced rule set by using forward orthogonal least squares model structure detection. In both stages, new A-optimality experimental design-based criteria we used. In the preprocessing stage, a lower bound of the A-optimality design criterion is derived and applied as a subset selection metric, but in the later stage, the A-optimality design criterion is incorporated into a new composite cost function that minimises model prediction error as well as penalises the model parameter variance. The utilisation of NeuDeC leads to unbiased model parameters with low parameter variance and the additional benefit of a parsimonious model structure. Numerical examples are included to demonstrate the effectiveness of this new modelling approach for high dimensional inputs.

Nonlinear model structure detection using optimum experimental design and orthogonal least squares

A very efficient learning algorithm for model subset selection is introduced based on a new composite cost function that simultaneously optimizes the model approximation ability and model adequacy. The derived model parameters are estimated via forward orthogonal least squares, but the subset selection cost function includes an A-optimality design criterion to minimize the variance of the parameter estimates that ensures the adequacy and parsimony of the final model. An illustrative example is included to demonstrate the effectiveness of the new approach.

Dual-orthogonal radial basis function networks for nonlinear time series prediction

A new structure of Radial Basis Function (RBF) neural network called the Dual-orthogonal RBF Network (DRBF) is introduced for nonlinear time series prediction. The hidden nodes of a conventional RBF network compare the Euclidean distance between the network input vector and the centres, and the node responses are radially symmetrical. But in time series prediction where the system input vectors are lagged system outputs, which are usually highly correlated, the Euclidean distance measure may not be appropriate. The DRBF network modifies the distance metric by introducing a classification function which is based on the estimation data set. Training the DRBF networks consists of two stages. Learning the classification related basis functions and the important input nodes, followed by selecting the regressors and learning the weights of the hidden nodes. In both cases, a forward Orthogonal Least Squares (OLS) selection procedure is applied, initially to select the important input nodes and then to select the important centres. Simulation results of single-step and multi-step ahead predictions over a test data set are included to demonstrate the effectiveness of the new approach.

Do in vivo terahertz imaging systems comply with safety guidelines?

Techniques for the coherent generation and detection of electromagnetic radiation in the far infrared, or terahertz, region of the electromagnetic spectrum have recently developed rapidly and may soon be applied for in vivo medical imaging. Both continuous wave and pulsed imaging systems are under development, with terahertz pulsed imaging being the more common method. Typically a pump and probe technique is used, with picosecond pulses of terahertz radiation generated from femtosecond infrared laser pulses, using an antenna or nonlinear crystal. After interaction with the subject either by transmission or reflection, coherent detection is achieved when the terahertz beam is combined with the probe laser beam. Raster scanning of the subject leads to an image data set comprising a time series representing the pulse at each pixel. A set of parametric images may be calculated, mapping the values of various parameters calculated from the shape of the pulses. A safety analysis has been performed, based on current guidelines for skin exposure to radiation of wavelengths 2.6 µm–20 mm (15 GHz–115 THz), to determine the maximum permissible exposure (MPE) for such a terahertz imaging system. The international guidelines for this range of wavelengths are drawn from two U.S. standards documents. The method for this analysis was taken from the American National Standard for the Safe Use of Lasers (ANSI Z136.1), and to ensure a conservative analysis, parameters were drawn from both this standard and from the IEEE Standard for Safety Levels with Respect to Human Exposure to Radio Frequency Electromagnetic Fields (C95.1). The calculated maximum permissible average beam power was 3 mW, indicating that typical terahertz imaging systems are safe according to the current guidelines. Further developments may however result in systems that will exceed the calculated limit. Furthermore, the published MPEs for pulsed exposures are based on measurements at shorter wavelengths and with pulses of longer duration than those used in terahertz pulsed imaging systems, so the results should be treated with caution.

A concept of approximated densities for efficient nonlinear estimation

This paper presents the theoretical development of a nonlinear adaptive filter based on a concept of filtering by approximated densities (FAD). The most common procedures for nonlinear estimation apply the extended Kalman filter. As opposed to conventional techniques, the proposed recursive algorithm does not require any linearisation. The prediction uses a maximum entropy principle subject to constraints. Thus, the densities created are of an exponential type and depend on a finite number of parameters. The filtering yields recursive equations involving these parameters. The update applies the Bayes theorem. Through simulation on a generic exponential model, the proposed nonlinear filter is implemented and the results prove to be superior to that of the extended Kalman filter and a class of nonlinear filters based on partitioning algorithms.

Applying the extended Kalman filter to systems described by nonlinear differential-algebraic equations

This paper describes a method for the state estimation of nonlinear systems described by a class of differential-algebraic equation models using the extended Kalman filter. The method involves the use of a time-varying linearisation of a semi-explicit index one differential-algebraic equation. The estimation technique consists of a simplified extended Kalman filter that is integrated with the differential-algebraic equation model. The paper describes a simulation study using a model of a batch chemical reactor. It also reports a study based on experimental data obtained from a mixing process, where the model of the system is solved using the sequential modular method and the estimation involves a bank of extended Kalman filters.

Dynamic integrated system optimization and parameter estimation for discrete time optimal control of nonlinear systems

An algorithm for solving nonlinear discrete time optimal control problems with model-reality differences is presented. The technique uses Dynamic Integrated System Optimization and Parameter Estimation (DISOPE), which achieves the correct optimal solution in spite of deficiencies in the mathematical model employed in the optimization procedure. A version of the algorithm with a linear-quadratic model-based problem, implemented in the C+ + programming language, is developed and applied to illustrative simulation examples. An analysis of the optimality and convergence properties of the algorithm is also presented.

Optimal control of nonlinear systems represented by differential algebraic equations

An iterative procedure is described for solving nonlinear optimal control problems subject to differential algebraic equations. The procedure iterates on an integrated modified simplified model based problem with parameter updating in such a manner that the correct solution of the original nonlinear problem is achieved.

A new approach for the solution of the optimal set-point tracking problem for nonlinear systems

In this paper, a discrete time dynamic integrated system optimisation and parameter estimation algorithm is applied to the solution of the nonlinear tracking optimal control problem. A version of the algorithm with a linear-quadratic model-based problem is developed and implemented in software. The algorithm implemented is tested with simulation examples.

Optimal control of nonlinear differential algebraic equation systems

A novel iterative procedure is described for solving nonlinear optimal control problems subject to differential algebraic equations. The procedure iterates on an integrated modified linear quadratic model based problem with parameter updating in such a manner that the correct solution of the original non-linear problem is achieved. The resulting algorithm has a particular advantage in that the solution is achieved without the need to solve the differential algebraic equations . Convergence aspects are discussed and a simulation example is described which illustrates the performance of the technique. 1. Introduction When modelling industrial processes often the resulting equations consist of coupled differential and algebraic equations (DAEs). In many situations these equations are nonlinear and cannot readily be directly reduced to ordinary differential equations.