Analysis of pollen material obtained from the Hirst-type apparatus, which is a tedious and labor-intensive process, is usually performed by hand under a microscope by specialists in palynology. This research evaluated the automatic analysis of pollen material performed based on digital microscopic photos. A deep neural network called YOLO was used to analyze microscopic images containing the reference grains of three taxa typical of Central and Eastern Europe. YOLO networks perform recognition and detection; hence, there is no need to segment the image before classification. The obtained results were compared to other deep learning object detection methods, i.e., Faster R-CNN and RetinaNet. YOLO outperformed the other methods, as it gave the mean average precision (mAP@.5:.95) between 86.8% and 92.4% for the test sets included in the study. Among the difficulties related to the correct classification of the research material, the following should be noted: significant similarities of the grains of the analyzed taxa, the possibility of their simultaneous occurrence in one image, and mutual overlapping of objects.

The risk of pollen-induced allergies can be determined and predicted based on data derived from pollen monitoring. Hirst-type samplers are sensors that allow airborne pollen grains to be detected and their number to be determined. Airborne pollen grains are deposited on adhesive-coated tape, and slides are then prepared, which require further analysis by specialized personnel. Deep learning can be used to recognize pollen taxa based on microscopic images. This paper presents a method for recognizing a taxon based on microscopic images of pollen grains, allowing the pollen monitoring process to be automated. In this research, a deep CNN (convolutional neural network) model was built from scratch. Publicly available deep neural network models, pre-trained on image data (not including microscopic pictures), were also used. The results show that even a simple deep learning model produces quite good results when the classification of pollen grain taxa is performed directly from the images. The best deep learning model achieved 97.88% accuracy in the difficult task of recognizing three types of pollen grains (birch, alder, and hazel) with similar structures. The derived models can be used to build a system to support pollen monitoring experts in their work.

Given an oval C in the plane, the $$\alpha $$α -isoptic $$C_\alpha $$C α of C is the plane curve composed of the points from which C can be seen under the angle $$\pi -\alpha $$π - α . We consider isoptics of ovals parametrized with the support function $$p(t)=a+\cos n t$$p ( t ) = a + cos n t , $$n\in \mathbb {N}$$n ∈ N , and present an example of an oval such that when $$\alpha $$α increases, the $$\alpha $$α -isoptics begin to be convex, then lose their convexity and finally are convex again along a curve intersecting the isoptics orthogonally. Next we give an example of a curve from the same family, for which the curvature of the isoptics changes its sign three times. These changes occur on the symmetry axes of the oval C and coincide with the orthogonal trajectories which start at the points with extremal curvature. Finally, we formulate the hypothesis concerning the general case where we expect $$n-1$$n - 1 convexity limit angles for the isoptics of an oval parametrized by $$p(t)=a+\cos n t$$p ( t ) = a + cos n t .

Https://doi.org/10.26485/0459-6854/2018/68.1/6 Isoptic curves have been known and studied since the 18th century. Nowadays they have been examined inter alia by Benko, Cie´slak, G´o´zd´z, Miernowski and Mozgawa in many papers for example in [1], [2], [3] and [7]. We want to propose a new point of view isoptics. For a given oval we consider a dual curve on Blaschke cylinder and we construct a dual curve for its isoptic. Some properties, for example the loss of convexity is easier to observe on the dual curve than on the given curve. From the analysis of properties of dual curves to isoptics we get a new form of the condition for the convexity of isoptic curves. https://doi.org/10.26485/0459-6854/2018/68.1/6 Izooptyki, to krzywe, które były znane i rozważane od XVIII wieku. W ostatnim półwieczu badali je między innymi przez Benko, Cieślak, Góźdź, Miernowski i Mozgawa w wielu pracach, na przykład w [1], [2], [3] i [7]. W tej publikacji chcemy zaproponować nowy sposób patrzenia na izooptyki. Dla danego owalu rozważamy jego krzywą dualną na cylindrze Blaschke’go i konstruujemy krzywą dualną do jego izooptyki. Niektóre własności, na przykład utratę wypukłości, łatwiej jest zaobserwować na krzywej dualnej niż na wyjściowej krzywej. Z analizy w lasności krzywych dualnych do izooptyk otrzymujemy nową postać warunku na wypukość izooptyk.