IMAGE SHAPE COMPARISON IN MOSAIC DIFFUSION MORPHOLOGIES

In this paper, developing the early proposed unified approach to the representation of morphological models, we show that since morphological models in the attribute representation have the same mathematical form as images, the morphological models themselves can be the subject of morphological analysis and can be directly compared in form with using morphological operators. In this case, the previously introduced formalism of mosaic diffusion morphology is used.In the framework of mosaic diffusion morphology, two alternative descriptions of the projection of the image on the form are considered, which are based on a clear model and a fuzzy model of the form respectively. It is shown that the projection operator in the second case is a one-sorted diffuse operator that makes direct comparision of model to model instead of image to model. In this case, a fuzzy mosaic model appears in this scheme as a projection of a clear mosaic model onto another clear mosaic model. Based on this shape-to-shape projection idea, we propose the new version of Pytiev morphology tools for shape comparison: the morphological shape difference map, the morphological quasi-distance between shapes, as well as the Morphological Shape Correlation Coefficient (MSCC). We show that MSCC from the resource parameters of the reciprocal model has exactly the same formula as the standard effective morphological correlation coefficient proposed earlier based on statistical averaging of projected images.

IMAGE AND SHAPE COMPARISON VIA MORPHOLOGICAL CORRELATION

A lot of image matching applications require image comparison to be invariant relative to intensity values variations. The Pyt’ev theory for Morphological Image Analysis (MIA) was developed based on image-to-shape matching with mosaic shape models. Within the framework of this theory, the problem of shape-to-shape comparison was previously considered too. The most sophisticated and weakest part of MIA theory is the comparison of mosaic shapes with some arbitrary restrictions described by graphs or relations. In this paper we consider the possible options for comparing images and shapes using morphological projection and morphological correlation. Our contribution is a new scheme of morphological shape-to-image projection and, correspondingly, the new morphological correlation coefficient (MCC) for shape-to-image correlation with restricted mosaic models. We also refine the expressions for shape-to-shape comparison.

Affine Shape Comparison using Different Distances

In this work, we propose to compare affine shape using Hausdorff distance (HD), Dynamic Time Warping (DTW), Frechet (DF), and Earth Mover distance (EMD). Where there is only a change in resolution shape distance are computed between shape coordinates because the distance is not invariant under rotation or affinity. In case of transformation, distances are calculated not between shape coordinates but between Arc length or Affine Arc length. Arc length is invariant under rotation while Affine Arc length is invariant under affinity. The main advantage is invariance under change of resolution, rotation, and affinity.

Application of high-resolution landmark-free morphometrics to a mouse model of Down Syndrome reveals a tightly localised cranial phenotype

Characterising phenotypes often requires quantification of anatomical shapes. Quantitative shape comparison (morphometrics) traditionally uses anatomical landmarks and is therefore limited by the number of landmarks and operator accuracy when landmarks are located manually. Here we apply a landmark-free method to characterise the craniofacial skeletal phenotype of the Dp1Tyb mouse model of Down syndrome (DS), validating it against a landmark-based approach. We identify cranial dysmorphologies in Dp1Tyb mice, especially smaller size and brachycephaly (front-back shortening) homologous to the human phenotype. The landmark-free phenotyping was less labour-intensive and required less user training than the landmark-based method. It also enabled mapping of local differences as planar expansion or shrinkage. This higher resolution and local mapping pinpointed reductions in interior mid-snout structures and occipital bones in this DS model that were not as apparent using a traditional landmark-based method. This approach could make morphometrics widely-accessible beyond traditional niches in zoology and palaeontology, especially in characterising mutant phenotypes.