Image analysis of real-time classification of cherry fruit from colour features

An image analysis algorithm for the classification of cherries in real time by processing their digitalized colour images was developed, and tested. A set of five digitalized images of colour pattern, corresponding to five colour classes defined for commercial cherries, was characterized. The algorithm performs the segmentation of the cheery image by rejecting the pixels of the background and keeping the image features corresponding to the coloured area of the fruit. A histogram analysis was carried out for the RGB and HSV colour spaces, where the Red and Hue components showed differences between each of the specified colour patterns of the exporting reference system. This information led to the development of a hybrid Bayesian classification algorithm based on the components R and H. Its accuracy was tested with a set of cherry samples within the colour range of interest. The algorithm was implemented by means of a real time C++ code in Microsoft Visual Studio environment. When testing, the algorithm showed a 100% effectiveness in classifying a sample set of cherries into the five standardized cherry classes. The components of the hardware-software system for implementing the methodology are low cost, thus ensuring an affordable commercial deployment.

Equitable colourings of Borel graphs

Hajnal and Szemerédi proved that if G is a finite graph with maximum degree $\Delta $ , then for every integer $k \geq \Delta +1$ , G has a proper colouring with k colours in which every two colour classes differ in size at most by $1$ ; such colourings are called equitable. We obtain an analogue of this result for infinite graphs in the Borel setting. Specifically, we show that if G is an aperiodic Borel graph of finite maximum degree $\Delta $ , then for each $k \geq \Delta + 1$ , G has a Borel proper k-colouring in which every two colour classes are related by an element of the Borel full semigroup of G. In particular, such colourings are equitable with respect to every G-invariant probability measure. We also establish a measurable version of a result of Kostochka and Nakprasit on equitable $\Delta $ -colourings of graphs with small average degree. Namely, we prove that if $\Delta \geq 3$ , G does not contain a clique on $\Delta + 1$ vertices and $\mu $ is an atomless G-invariant probability measure such that the average degree of G with respect to $\mu $ is at most $\Delta /5$ , then G has a $\mu $ -equitable $\Delta $ -colouring. As steps toward the proof of this result, we establish measurable and list-colouring extensions of a strengthening of Brooks’ theorem due to Kostochka and Nakprasit.

Conspecifics of the Striped Lava Lizard are able to distinguish sex and male colour morphs in apparently homogeneous dull dorsal colouration

Animal colouration plays a key role in inter and intraspecific interactions, pre-eminently in mate signalling. When multiple types of colouration occur within sexes it is possible that they show alternative reproductive strategies. In lizards, most colouration studies do not incorporate how colour is perceived by conspecifics. Here, we used unbiased colour analysis methods (spectrophotometry and visual modelling) to test for sexual dimorphism and within male dichromatism in the Striped Lava Lizard. We found that males express two distinct colourations that are different from females in several dorsal and ventral body regions. Our results showed UV reflection at the throat, an important body region for signalling. Ventral patches, the coloured badge seen in adult males of Tropidurus spp., have two distinct colour classes within males (Y and B males). Morphs are best discriminated by blue and yellow chroma, and brightness. Body size had little influence on colouration, suggesting that colour may be linked to inheritance rather than growth. Our study clearly shows sexual dichromatism and the existence of colour morphs in this species. Moreover, morph differences in colouration are perceptible by conspecifics. These differences are not only between ventral patches, but also in other body parts such as the dorsum, previously considered as cryptic by human observers. We suggest that colouration at the ventral patches and throat might play a role in intraspecific interactions. Patches increase colour intensity during breeding season and are likely to be costly by pigment-based expression, whereas throat’s UV reflection might have a cost infringed by conspicuousness.

Discrete or indiscrete? Redefining the colour polymorphism of the land snail Cepaea nemoralis

Biologists have long tried to describe and name the different phenotypes that make up the exuberant colour polymorphism of the land snail Cepaea nemoralis. Traditionally, the view is that the ground colour is one of a few major colour classes, either yellow, pink or brown, but in practise it is frequently difficult to distinguish the colours, and consistently define different shades of the same colour. To understand whether colour variation is continuous, and to investigate how the variation may be perceived by an avian predator, we applied psychophysical models of colour vision to shell reflectance measures. The main finding is that both achromatic and chromatic variation are indiscrete, being continuously distributed over many perceptual units, with the major axis of chromatic variation representing differences in saturation, or purity of colour. Nonetheless, clustering analysis based on the density of the distribution revealed three groups, roughly corresponding to human-perceived yellow, pink and brown shells. There is also large-scale geographic variation between these morphs across Europe, and some covariance between shell colour and banding patterns. Although further studies are necessary to understand the evolutionary origins and impact of natural selective upon this variation, the observation of continuous variation in colour is intriguing, given that the underlying supergene that determines colour should prevent phenotypes from “dissolving” into continuous trait distributions.

Deciding Relaxed Two-Colourability: A Hardness Jump

We study relaxations of proper two-colourings, such that the order of the induced monochromatic components in one (or both) of the colour classes is bounded by a constant. A colouring of a graph G is called (C1, C2)-relaxed if every monochromatic component induced by vertices of the first (second) colour is of order at most C1 (C2, resp.). We prove that the decision problem ‘Is there a (1, C)-relaxed colouring of a given graph G of maximum degree 3?’ exhibits a hardness jump in the component order C. In other words, there exists an integer f(3) such that the decision problem is NP-hard for every 2 ≤ C < f(3), while every graph of maximum degree 3 is (1, f(3))-relaxed colourable. We also show f(3) ≤ 22 by way of a quasilinear time algorithm, which finds a (1, 22)-relaxed colouring of any graph of maximum degree 3. Both the bound on f(3) and the running time greatly improve earlier results. We also study the symmetric version, that is, when C1 = C2, of the relaxed colouring problem and make the first steps towards establishing a similar hardness jump.

A Short Proof of the Hajnal–Szemerédi Theorem on Equitable Colouring

A proper vertex colouring of a graph is equitable if the sizes of colour classes differ by at most one. We present a new shorter proof of the celebrated Hajnal–Szemerédi theorem: for every positive integer r, every graph with maximum degree at most r has an equitable colouring with r+1 colours. The proof yields a polynomial time algorithm for such colourings.

Genetic Diversity of Hair Colour in Horses

The main aim of this study was to analyze sources of variability for coat colour expressed as a quantitative trait as well as to determine non genetic factors influencing horse colour variation and shades. Traditional Hungarian horse breeds such as Lipizzan (grey), Gidran (chestnut), Shagya Arabian and Arabian Pure Bred (grey) and Nonius (bay and black) horses were involved in the current study. We report results using direct measurements of horse coat colour using objective colorimetric dimensions and a spectrophotometer for determining hair melanin. Correlation analysis indicated that the single biological component that correlated best with the total melanin content of horse hair is the L* value (r=-0.858, p<0.0001). Subjective colour classes and coat colour variables L* and a* were obviously related, with R2 values of 0.88 and 0.46 respectively, with a lower R2 for b* of 0.22 (all p<0.001).