Back to the Future: Economic Self-Organisation and Maximum Entropy Prediction

This paper shows that signal restoration methodology is appropriate for predicting the equilibrium state of certain economic systems. A formal justification for this is provided by proving the existence of finite improvement paths in object allocation problems under weak assumptions on preferences, linking any initial condition to a Nash equilibrium. Because a finite improvement path is made up of a sequence of systematic best-responses, backwards movement from the equilibrium back to the initial condition can be treated like the realisation of a noise process. This underpins the use of signal restoration to predict the equilibrium from the initial condition, and an illustration is provided through an application of maximum entropy signal restoration to the Schelling model of segregation

Object-based assessment of tree attributes of Acacia tortilis in Bou-Hedma, Tunisia

Acacia tortilis subsp. raddiana represents the most important woody species in the pre-Saharan zone. It is the only forest tree persisting on the edge of the desert. Due to tree/environment interactions, canopy sub-habitats arise, enabling an increased storage of soil water, soil nutrients and soil oxygen. Depending on their density, they can also reduce erosion and reverse desertification. Soil erosion and desertification are the main problems faced by the UNESCO Biosphere Reserve in South-Tunisia (Bou-Hedma National Park). The restoration of the original woodland cover to combat desertification (particularly) by afforestation and reforestation of Acacia tortilis goes hand in hand with a climate change in the Biosphere Reserve, also influencing rural population outside the Biosphere Reserve. In order to study the different effects of woodland restoration in Bou-Hedma, the number of Acacia trees and their attributes have to be known. High resolution satellite imagery (GeoEye-1), was used with a GEOBIA approach. Field measurement of bole diameter, crown diameter and tree height were collected at > 400 locations. After segmentation, correlations with > 200 object features and tree attributes were calculated. For crown diameter and tree height, high correlations were observed with the features area and GLCM Entropy Layer 4 (90 degrees). Relations between these features and measured tree attributes were modeled, resulting in RMSE values of resp. 1.47 m and 1.62 m for crown diameter estimation and 0.92 m for tree height. The results show that a GEOBIA working strategy is suitable for estimating tree attributes in open forests in semi-arid regions

Information theoretic approach for assessing image fidelity in photon-counting arrays

The method of photon-counting integral imaging has been introduced recently for three-dimensional object sensing, visualization, recognition and classification of scenes under photon-starved conditions. This paper presents an information-theoretic model for the photon-counting imaging (PCI) method, thereby providing a rigorous foundation for the merits of PCI in terms of image fidelity. This, in turn, can facilitate our understanding of the demonstrated success of photon-counting integral imaging in compressive imaging and classification. The mutual information between the source and photon-counted images is derived in a Markov random field setting and normalized by the source-image’s entropy, yielding a fidelity metric that is between zero and unity, which respectively corresponds to complete loss of information and full preservation of information. Calculations suggest that the PCI fidelity metric increases with spatial correlation in source image, from which we infer that the PCI method is particularly effective for source images with high spatial correlation; the metric also increases with the reduction in photon-number uncertainty. As an application to the theory, an image-classification problem is considered showing a congruous relationship between the fidelity metric and classifier’s performance

Optimum non linear binary image restoration through linear grey-scale operations

Non-linear image processing operators give excellent results in a number of image processing tasks such as restoration and object recognition. However they are frequently excluded from use in solutions because the system designer does not wish to introduce additional hardware or algorithms and because their design can appear to be ad hoc. In practice the median filter is often used though it is rarely optimal. This paper explains how various non-linear image processing operators may be implemented on a basic linear image processing system using only convolution and thresholding operations. The paper is aimed at image processing system developers wishing to include some non-linear processing operators without introducing additional system capabilities such as extra hardware components or software toolboxes. It may also be of benefit to the interested reader wishing to learn more about non-linear operators and alternative methods of design and implementation. The non-linear tools include various components of mathematical morphology, median and weighted median operators and various order statistic filters. As well as describing novel algorithms for implementation within a linear system the paper also explains how the optimum filter parameters may be estimated for a given image processing task. This novel approach is based on the weight monotonic property and is a direct rather than iterated method

Deep Dictionary Learning: A PARametric NETwork Approach

Deep dictionary learning seeks multiple dictionaries at different image scales to capture complementary coherent characteristics. We propose a method for learning a hierarchy of synthesis dictionaries with an image classification goal. The dictionaries and classification parameters are trained by a classification objective, and the sparse features are extracted by reducing a reconstruction loss in each layer. The reconstruction objectives in some sense regularize the classification problem and inject source signal information in the extracted features. The performance of the proposed hierarchical method increases by adding more layers, which consequently makes this model easier to tune and adapt. The proposed algorithm furthermore, shows remarkably lower fooling rate in presence of adversarial perturbation. The validation of the proposed approach is based on its classification performance using four benchmark datasets and is compared to a CNN of similar size

New adaptive iterative image restoration algorithm

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