Comparison of statistical properties for various morphological filters based on mosaic image shape models

We consider the statistical properties of different mosaic filters. We demonstrate that in Pitiev's morphology, the measure of shape complexity is directly related to the shape simplicity measure based on morphological correlation coefficient (MCC). Based on MCC, we introduce the normalized morphological simplification index (NMSI). Using NMSI, we show that the simpler the mosaic shape, the more shape simplification is provided by the corresponding Pyt'ev projector. For the examples of mean and median mosaic filters, we address the problem of different operator comparison. In this context we introduce the concept of statistically simplifying morphological operators. Morphological correlation of mosaic shape and diffusion mosaic operator is considered. We prove that the NMSI for the diffusion mosaic operator is not related to the complexity for the corresponding diffusion shape kernel. Thus, a principal qualitative difference in the relationship between relational and operator models for diffuse and projective mosaic linear filters is demonstrated.

Quantifying the importance of a realistic tomato (Solanum lycopersicum) leaflet shape for 3-D light modelling

Background and Aims Leaflet shapes of tomato plants (Solanum lycopersicum) have been reduced to simple geometric shapes in previous functional–structural plant models (FSPMs) in order to facilitate measurements and reduce the time required to reconstruct the plant virtually. The level of error that such simplifications introduce remains unaddressed. This study therefore aims to quantify the modelling error associated with simplifying leaflet shapes. Methods Realistic shapes were implemented in a static tomato FSPM based on leaflet scans, and simulation results were compared to simple geometric shapes used in previous tomato FSPMs in terms of light absorption and gross photosynthesis, for both a single plant and a glasshouse scenario. Key Results The effect of simplifying leaflet shapes in FSPMs leads to small but significant differences in light absorption, alterations of canopy light conditions and differences in photosynthesis. The magnitude of these differences depends on both the type of leaflet shape simplification used and the canopy shape and density. Incorporation of realistic shapes requires a small increase in initial measurement and modelling work to establish a shape database and comes at the cost of a slight increase in computation time. Conclusions Our findings indicate that the error associated with leaflet shape simplification is small, but often unpredictable, and is affected by plant structure but also lamp placement, which is often a primary optimization goal of these static models. Assessment of the cost–benefit of realistic shape inclusion shows relatively little drawbacks for a decrease in model uncertainty.

REVERSE MODELING OF CULTURAL HERITAGE: PIPELINE AND BOTTLENECKS

<p><strong>Abstract.</strong> The present work is suggested as a contribution to the debate on Reverse Modeling (RM) topic in the Cultural Heritage field. It wants to test the methodology, the limits and the bottlenecks of the RM pipeline in the architectural field, with particular attention to the geometric shapes reading and interpretation. The mathematical reconstruction of architectural models represents an overlaid result of anthropic and natural transformations framed inside a complex process of shape simplification and surface generation. This pipeline must be supported by a careful Heritage reading by means of architecture rules, both preserving the actual shape and the original intent of the building designer. The integration of these last two aspects make the process of RM applied to CH extremely complex. It involves a cognitive activity aimed at choosing on the one hand the best 3D survey technique to obtain reliable 3D data, on the other hand reaching a suitable architectural knowledge for achieving a plausible modeling result. The research presented describes a RM process applied to an ecclesiastical architecture, highlighting some key passages: an integrated survey approach to extract geometrical information, data analysis and generation of a mathematical 3D model, reliable from both a formal and cultural point of view.</p>