We prove a very general sharp inequality of the H\"older--Young--type for functions defined ... more We prove a very general sharp inequality of the H\"older--Young--type for functions defined on infinite dimensional Gaussian spaces. We begin by considering a family of commutative products for functions which interpolates between the point--wise and Wick products; this family arises naturally in the context of stochastic differential equations, through Wong--Zakai--type approximation theorems, and plays a key role in some generalizations of the Beckner--type Poincar\'e inequality. We then obtain a crucial integral representation for that family of products which is employed, together with a generalization of the classic Young inequality due to Lieb, to prove our main theorem. We stress that our main inequality contains as particular cases the H\"older inequality and Nelson's hyper-contractive estimate, thus providing a unified framework for two fundamental results of the Gaussian analysis.
Automatic extraction of cartographic features from aerial or satellite images is an important iss... more Automatic extraction of cartographic features from aerial or satellite images is an important issue of recent research primarily for their potential use in geographic information systems (GIS) and for creating archaeological sites prediction models. The view from above allows to recognize archaeological features, not visible on the ground, by the analysis of crops variations in an expanded spatial context. Automatic algorithms would be very useful to support archaeologists during the time consuming task of visual interpretation and the manual digitalization of large aerial images. In this paper we present some automatic and semi-automatic approaches for trace extraction, based on different methodologies such as active contours and statistical analysis. The application of standard image analysis procedures for trace extraction is generally unsuccessfull due to their frequent poor visibility, intricate texture, background inhomogeneity, not well-defined boundaries, similarity with oth...
ABSTRACT The paper describes the developed hardware and software components of a computer vision ... more ABSTRACT The paper describes the developed hardware and software components of a computer vision system that extracts colour parameters from calibrated colour images and identifies non-destructively the different quality levels exhibited by lettuce (either whole or fresh-cut) during storage. Several colour parameters extracted by computer vision system have been evaluated to characterize the product quality levels. Among these, brown on total and brown on white proved to achieve a good identification of the different quality levels on whole and fresh-cut lettuce (P-value < 0.0001). In particular, these two parameters were able to discriminate three levels: very good or good products (quality levels from 5 to 4), samples at the limit of marketability (quality level of 3) and waste items (quality levels from 2 to 1). Quality levels were also chemically and physically characterized. Among the parameters analysed, ammonia content proved to discriminate the marketable samples from the waste in both product's typologies (either fresh-cut or whole); even the two classes of waste were well discriminated by ammonia content (P-value < 0.0001). A function that infers quality levels from the extracted colour parameters has been identified using a multi-regression model (R-2 = 0.77). Multi-regression also identified a function that predicts the level of ammonia (an indicator of senescence) in the iceberg lettuce from a colour parameter provided by the computer vision system (R-2 = 0.73), allowing a non-destructive evaluation of a chemical parameter that is particularly useful for the objective assessment of lettuce quality. The developed computer vision system offers flexible and simple non-destructive tool that can be employed in the food processing industry to monitor the quality and shelf life of whole and fresh-cut lettuce in a reliable, objective and quantitative way.
ABSTRACT The aim of this paper is to generalize two important results known for the Stratonovich ... more ABSTRACT The aim of this paper is to generalize two important results known for the Stratonovich and Itô integrals to any stochastic integral obtained as limit of Riemann sums with arbitrary evaluating point: the ordinary chain rule for certain nonlinear functions of the Brownian motion and the Wong–Zakai approximation theorem. To this scope we begin by introducing a new family of products for smooth random variables which reduces for specific choices of a parameter to the pointwise and to the Wick products. We show that each product in that family is related in a natural way to a precise choice of the evaluating point in the above mentioned Riemann sums and hence to a certain notion of stochastic integral. Our chain rule relies on a new probabilistic representation for the solution of the heat equation while the Wong–Zakai type theorem follows from a reduction method for quasi-linear SDEs together with a formula of Gjessing’s type.
We prove a very general sharp inequality of the H\"older--Young--type for functions defined ... more We prove a very general sharp inequality of the H\"older--Young--type for functions defined on infinite dimensional Gaussian spaces. We begin by considering a family of commutative products for functions which interpolates between the point--wise and Wick products; this family arises naturally in the context of stochastic differential equations, through Wong--Zakai--type approximation theorems, and plays a key role in some generalizations of the Beckner--type Poincar\'e inequality. We then obtain a crucial integral representation for that family of products which is employed, together with a generalization of the classic Young inequality due to Lieb, to prove our main theorem. We stress that our main inequality contains as particular cases the H\"older inequality and Nelson's hyper-contractive estimate, thus providing a unified framework for two fundamental results of the Gaussian analysis.
Automatic extraction of cartographic features from aerial or satellite images is an important iss... more Automatic extraction of cartographic features from aerial or satellite images is an important issue of recent research primarily for their potential use in geographic information systems (GIS) and for creating archaeological sites prediction models. The view from above allows to recognize archaeological features, not visible on the ground, by the analysis of crops variations in an expanded spatial context. Automatic algorithms would be very useful to support archaeologists during the time consuming task of visual interpretation and the manual digitalization of large aerial images. In this paper we present some automatic and semi-automatic approaches for trace extraction, based on different methodologies such as active contours and statistical analysis. The application of standard image analysis procedures for trace extraction is generally unsuccessfull due to their frequent poor visibility, intricate texture, background inhomogeneity, not well-defined boundaries, similarity with oth...
ABSTRACT The paper describes the developed hardware and software components of a computer vision ... more ABSTRACT The paper describes the developed hardware and software components of a computer vision system that extracts colour parameters from calibrated colour images and identifies non-destructively the different quality levels exhibited by lettuce (either whole or fresh-cut) during storage. Several colour parameters extracted by computer vision system have been evaluated to characterize the product quality levels. Among these, brown on total and brown on white proved to achieve a good identification of the different quality levels on whole and fresh-cut lettuce (P-value < 0.0001). In particular, these two parameters were able to discriminate three levels: very good or good products (quality levels from 5 to 4), samples at the limit of marketability (quality level of 3) and waste items (quality levels from 2 to 1). Quality levels were also chemically and physically characterized. Among the parameters analysed, ammonia content proved to discriminate the marketable samples from the waste in both product's typologies (either fresh-cut or whole); even the two classes of waste were well discriminated by ammonia content (P-value < 0.0001). A function that infers quality levels from the extracted colour parameters has been identified using a multi-regression model (R-2 = 0.77). Multi-regression also identified a function that predicts the level of ammonia (an indicator of senescence) in the iceberg lettuce from a colour parameter provided by the computer vision system (R-2 = 0.73), allowing a non-destructive evaluation of a chemical parameter that is particularly useful for the objective assessment of lettuce quality. The developed computer vision system offers flexible and simple non-destructive tool that can be employed in the food processing industry to monitor the quality and shelf life of whole and fresh-cut lettuce in a reliable, objective and quantitative way.
ABSTRACT The aim of this paper is to generalize two important results known for the Stratonovich ... more ABSTRACT The aim of this paper is to generalize two important results known for the Stratonovich and Itô integrals to any stochastic integral obtained as limit of Riemann sums with arbitrary evaluating point: the ordinary chain rule for certain nonlinear functions of the Brownian motion and the Wong–Zakai approximation theorem. To this scope we begin by introducing a new family of products for smooth random variables which reduces for specific choices of a parameter to the pointwise and to the Wick products. We show that each product in that family is related in a natural way to a precise choice of the evaluating point in the above mentioned Riemann sums and hence to a certain notion of stochastic integral. Our chain rule relies on a new probabilistic representation for the solution of the heat equation while the Wong–Zakai type theorem follows from a reduction method for quasi-linear SDEs together with a formula of Gjessing’s type.
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Papers by Paolo Da Pelo