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1

Sztuczna inteligencja – pomoc w wykryciu retinopatii cukrzycowej?

Kaczmarek Ewa

Optyka

|

2021

|

Nr 6

48--49

PL

Cukrzyca jest chorobą ogólnoustrojową, prowadzi do zmian w ukrwieniu i odżywianiu tkanek. Jej częstym okulistycznym powikłaniem jest retinopatia cukrzycowa (ang. diabetic retinopathy, DR). Amerykańskie Stowarzyszenie Diabetologiczne podało, że retinopatia cukrzycowa jest najczęstszą przyczyną ślepoty u osób w wieku produkcyjnym na świecie. W trakcie jej trwania dochodzi do uszkodzenia i powstania patologicznych naczyń krwionośnych siatkówki. Retinopatię cukrzycową dzielimy na trzy stadia: nieproliferacyjną, przedproliferacyjną i proliferacyjną. Początkowo DR, mimo zmian na dnie oka, nie daje objawów. Jeśli leczenie zostanie wdrożone, gdy zmiany będą zaawansowane, może być ono mało skuteczne, dlatego tak ważna jest szybka i prawidłowa diagnostyka DR.

2

Nieodwracalnie przemijające widzenie

Chylewska Justyna

Optyka

|

2021

|

Nr 1

52--56

PL

Zarówno w Polsce, jak i na świecie jest wzrost liczby osób starszych, czyli powyżej 60. roku życia. Na całym świecie prognozuje się, że liczba osób starszych wzrośnie z 605 mln w 2000 roku do około 2 mld w 2050 roku. W Polsce w 2019 roku populacja osób 60+ stanowiła 9,39 mln, czyli ponad 1/4 społeczeństwa całego kraju, która wyniosła 38,4 mln osób. Porównując z 2015 rokiem można zauważyć wzrost liczby osób w wieku senioralnym o ponad 900 tys. osób. Przewiduje się, że w 2050 roku osób powyżej 65 lat będzie około 11,1 mln spośród 33,95 mln Polaków, co stanowi 32,7%. Wydłuża się także średnia wieku umieralności, która wynosi w Polsce dla kobiet prawie 82 lata, a dla mężczyzn 74 lata (2019 rok). W ciągu 30 lat jest to wydłużenie czasu trwania życia o odpowiednio blisko osiem i siedem lat.

3

Microaneurysm detection in fundus images based on a novel end-to-end convolutional neural network

Liao Yinhan, Xia Haiying, Song Shuxiang, Li Haisheng

Biocybernetics and Biomedical Engineering

|

2021

|

Vol. 41, no. 2

589--604

EN

Microaneurysms are the earliest symptom of diabetic retinopathy and play an important role in the screening of diabetic retinopathy. However, because of the complex background, automatic detection microaneurysm in fundus images is a challenging task. Firstly, motivated by the characteristics of microaneurysm, a novel deep convolutional encoder-decoder network for microaneurysm detection is designed to locate the MAs by the differences between the skip connection in the network. Then, a weighted dice loss, termed the smooth dice loss, is presented to put more focus on misclassified microaneurysms. Finally, an activation function with a long tail is used to produce an accurate probability map for MA detection. Plenty of experiments, conducted on the Retinopathy Online Challenge data-set and the e-ophtha-MA dataset, demonstrate that the proposed model achieves the comparable performance to the existing state-of-the-art methods on microaneurysm detection with only one-hundredth the running time compared with its counterparts. The proposed method is simple and effective, guarantees the performance while shortening the test time. It indicates the potential application in the auxiliary diagnosis of diabetic retinopathy screening.

4

Retinopatia cukrzycowa najczęstszą przyczyną utraty wzroku u osób w wieku produkcyjnym

Lemanik Aleksandra

Optyka

|

2020

|

Nr 4

50--52

PL

Cukrzyca jest zaliczana do chorób cywilizacyjnych. W Polsce według danych Głównego Urzędu Statystycznego z 2017 roku choruje ponad 2,1 mln (7%) osób powyżej 15. r.ż. [1]. Każdego roku liczba ta wzrasta o około 400 tys., a ponadto szacuje się, że 25% osób nie wie o swojej chorobie. Cukrzyca jest już nazywana epidemią.

5

Retinal vasculature segmentation and measurement framework for color fundus and SLO images

Pachade Samiksha, Porwal Prasanna, Kokare Manesh, Giancardo Luca, Meriaudeau Fabrice

Biocybernetics and Biomedical Engineering

|

2020

|

Vol. 40, no. 3

865--900

EN

The change in vascular geometry is an indicator of various health issues linked with vision and cardiovascular risk factors. Early detection and diagnosis of these changes can help patients to select an appropriate treatment option when the disease is in its primary phase. Automatic segmentation and quantification of these vessels would decrease the cost and eliminate inconsistency related to manual grading. However, automatic detection of the vessels is challenging in the presence of retinal pathologies and non-uniform illumination, two common occurrences in clinical settings. This paper presents a novel framework to address the issue of retinal blood vessel detection and width measurement under these challenging circumstances and also on two different imaging modalities: color fundus imaging and Scanning Laser Ophthalmoscopy (SLO). In this framework, initially, vessel enhancement is done using linear recursive filtering. Then, a unique combination of morphological operations, background estimation, and iterative thresholding are applied to segment the blood vessels. Further, vessel diameter is estimated in two steps: firstly, vessel centerlines are extracted using the graph-based algorithm. Then, vessel edges are localized from the image profiles, by utilizing spline fitting to obtain vascular orientations and then finding the zero-crossings. Extensive experiments have been carried out on several publicly accessible datasets for vessel segmentation and diameter measurement, i.e., DRIVE, STARE, IOSTAR, RC-SLO and REVIEW dataset. Results demonstrate the competitive and comparable performance than earlier methods. The encouraging quantitative and visual performance of the proposed framework makes it an important component of a decision support system for retinal images.

6

Modified U-Net architecture for semantic segmentation of diabetic retinopathy images

Sambyal Nitigya, Saini Poonam, Syal Rupali, Gupta Varun

Biocybernetics and Biomedical Engineering

|

2020

|

Vol. 40, no. 3

1094--1109

EN

Segmentation of lesions from fundus images is an essential prerequisite for accurate severity assessment of diabetic retinopathy. Due to variation in morphologies, number and size of lesions, the manual grading process becomes extremely challenging and time-consuming. This necessitates the need of an automatic segmentation system that can precisely define the region of interest boundaries and assist ophthalmologists in speedy diagnosis along with diabetic retinopathy severity grading. The paper presents a modified U-Net architecture based on residual network and employs periodic shuffling with sub-pixel convolution initialized to convolution nearest neighbour resize. The proposed architecture has been trained and validated for microaneurysm and hard exudate segmentation on two publicly available datasets namely IDRiD and e-ophtha. For IDRiD dataset, the network obtains 99.88% accuracy, 99.85% sensitivity, 99.95% specificity and dice score of 0.9998 for both microaneurysm and exudate segmentation. Further, when trained on e-ophtha and validated on IDRiD dataset, the network shows 99.98% accuracy, 99.88% sensitivity, 99.89% specificity and dice score of 0.9998 for microaneurysm segmentation. For exudates segmen-tation, the model obtained 99.98% accuracy, 99.88% sensitivity, 99.89% specificity and dice score of 0.9999, when trained on e-ophtha and validated on IDRiD dataset. In comparison to existing literature, the proposed model provides state-of-the-art results for retinal lesion segmentation.

7

Robust intensity variation and inverse surface adaptive thresholding techniques for detection of optic disc and exudates in retinal fundus images

Karkuzhali S., Manimegalai D.

Biocybernetics and Biomedical Engineering

|

2019

|

Vol. 39, no. 3

753--764

EN

Diabetic Retinopathy (DR) is an adverse change in retinal blood vessels leads to blindness for diabetic patients without any symptoms. Diabetes is characterized by imbalance level of glucose in the human body. The optic disc (OD) is the major retinal landmark. Localization of OD is an important step in fundus image analysis and to develop Computer Aided Diagnosis tool for DR. OD center detection is necessary to reduce false positive rate in the detection of exudates (EXs). EXs is the white lesion present in the retina which is the early symptom for the diagnosis of DR. OD is detected using intensity variation algorithm and EXs is segmented using inverse surface adaptive thresholding algorithm. This algorithm achieves better result in localizing OD and segmenting EXs when compared to literature-reviewed methods. The maximum intensity variance method is used to locate OD with average ACC of 96.54%, 98.65%, 98.12%, 99.23%, 99.81% and 98.47% in DIARETDB0, DIARETDB1, MESSIDOR, DRIVE, STARE and Bejan Singh Eye Hospital databases with less computation time of 102 ms, 108 ms, 120 ms, 93 ms, 110 ms and 131 ms. The inverse surface adaptive thresholding method has achieved an SE of 97.43%, 98.87%, 99.12%, 97.21%, 98.72%, and 96.63%, a SPE of 91.56%, 92.31%, 90.21%, 90.14%, 89.58%, 92.56% and an ACC of 99.34%, 99.67%, 98.34%, 98.87%, 99.13%, 98.34% for DIARETDB0, DIARETDB1, MESSIDOR, DRIVE, STARE and Bejan Singh Eye Hospital databases respectively.

8

Diagnozowanie stanu retinopatii cukrzycowej przy pomocy głębokich sieci neuronowych

Jarzembiński B., Kwasigroch A., Grochowski M.

Zeszyty Naukowe Wydziału Elektrotechniki i Automatyki Politechniki Gdańskiej

|

2018

|

Nr 60

37--40

PL

W referacie opisano problem wykrywania oraz klasyfikacji stanu retinopatii cukrzycowej ze zdjęć dna oka przy pomocy głębokich sieci neuronowych. Retinopatia cukrzycowa jest chorobą oczu często występującą u osób z cukrzycą. Nieleczona prowadzi do uszkodzenia wzroku, a nawet ślepoty. W pracy badawczej opracowano system wykrywania retinopatii cukrzycowej na podstawie zdjęć dna oka. Opracowana sieć neuronowa przypisuje stan choroby w 5 stopniowej skali – od braku choroby do najbardziej zaawansowanego stanu choroby. Zaproponowano specjalny system kodowania klas w celu uchwycenia wielkości różnicy pomiędzy rzeczywistymi a predykowanymi stanami choroby. Uzyskano wysokie wyniki klasyfikacji na zbiorze testowym. W celu oceny skuteczności działania systemu wykorzystano miary statystyczne takie jak ważona Kappa i dokładność.

EN

In the paper we described computer aided detection system of diabetic retinopathy based on fundus photos of retina. Diabetic retinopathy is an eye disease associated with diabetes. Non-treated diabetic retinopathy leads to sight degeneration and even blindness. Early detection is crucial due to provide effective treatment. Currently, diabetic retinopathy detection is time consuming process, done manualy by medical specialist. The disease is dangerous issue in places where the availability of phisicians is limited. We employed the computer system that detect diabetic retinopathy and assess a stage of the disease based on retinal photo of fundus. We used one of the best image classification system – deep neural networks. Employed system assess the stage of the disease in 5 level scale – from absence of disease to the most severe stage of disease. We employed transfer learning and data augmentation to enhance classification result. Moreover we proposed special class coding system to catch the difference between real and predicted stage of disease. We tested employed system using different statistical measures like accuracy, sensitivity, specificity and Kappa score.

9

Estimation of severity level of non-proliferative diabetic retinopathy for clinical aid

Kaur J., Mittal D.

Biocybernetics and Biomedical Engineering

|

2018

|

Vol. 38, no. 3

708--732

EN

Diabetic retinopathy, a symptomless complication of diabetes, is one of the significant causes of vision impairment in the world. The early detection and diagnosis can reduce the occurrence of severe vision loss due to diabetic retinopathy. The diagnosis of diabetic retinopathy depends on the reliable detection and classification of bright and dark lesions present in retinal fundus images. Therefore, in this work, reliable segmentation of lesions has been performed using iterative clustering irrespective of associated heterogeneity, bright and faint edges. Afterwards, a computer-aided severity level detection method is proposed to aid ophthalmologists for appropriate treatment and effective planning in the diagnosis of non-proliferative diabetic retinopathy. This work has been performed on a composite database of 5048 retinal fundus images having varying attributes such as position, dimensions, shapes and color to make a reasonable comparison with state-of-the-art methods and to establish generalization capability of the proposed method. Experimental results on per-lesion basis show that the proposed method outperforms state-of-the methods with an average sensitivity/specificity/accuracy of 96.41/96.57/94.96 and 95.19/96.24/96.50 for bright and dark lesions respectively on composite database. Individual per-image based class accuracies delivered by the proposed method: No DR-95.9%, MA-98.3%, HEM-98.4%, EXU-97.4% and CWS-97.9% demonstrate the clinical competence of the method. Major contribution of the proposed method is that it efficiently grades the severity level of diabetic retinopathy in spite of huge variations in retinal images of different databases. Additionally, the substantial combined performance of these experiments on clinical and open source benchmark databases support a strong candidature of the proposed method in the diagnosis of non-proliferative diabetic retinopathy.

10

A generalized method for the segmentation of exudates from pathological retinal fundus images

Kaur J., Mittal D.

Biocybernetics and Biomedical Engineering

|

2018

|

Vol. 38, no. 1

27--53

EN

Diabetic retinopathy, an asymptomatic complication of diabetes, is one of the leading causes of blindness in the world. The exudates, abnormal leaked fatty deposits on retina, are one of the most prevalent and earliest clinical signs of diabetic retinopathy. In this paper, a generalized exudates segmentation method to assist ophthalmologists for timely treatment and effective planning in the diagnosis of diabetic retinopathy is developed. The main contribution of the proposed method is the reliable segmentation of exudates using dynamic decision thresholding irrespective of associated heterogeneity, bright and faint edges. The method is robust in the sense that it selects the threshold value dynamically irrespective of the large variations in retinal fundus images from varying databases. Since no performance comparison of state of the art methods is available on common database, therefore, to make a fair comparison of the proposed method, this work has been performed on a diversified database having 1307 retinal fundus images of varying characteristics namely: location, shapes, color and sizes. The database comprises of 649 clinically acquired retinal fundus images from eye hospital and 658 retinal images from publicly available databases such as STARE, MESSIDOR, DIARETDB1 and e-Optha EX. The segmentation results are validated by performing two sets of experiments namely: lesion based evaluation criteria and image based evaluation criteria. Experimental results at lesion level show that the proposed method outperforms other existing methods with a mean sensitivity/specificity/accuracy of 88.85/96.15/93.46 on a composite database of retinal fundus images. The segmentation results for image-based evaluation with a mean sensitivity/specificity/accuracy of 94.62/ 98.64/96.74 respectively prove the clinical effectiveness of the method. Furthermore, the significant collective performance of these experiments on clinically as well as publicly available standard databases proves the generalization ability and the strong candidature of the proposed method in the real-time diagnosis of diabetic retinopathy.

11

Robust and accurate optic disk localization using vessel symmetry line measure in fundus images

Panda R., Puhan N. B., Panda G.

Biocybernetics and Biomedical Engineering

|

2017

|

Vol. 37, no. 3

466--476

EN

Accurate optic disk (OD) localization is an important step in fundus image based computer-aided diagnosis of glaucoma and diabetic retinopathy. Robust OD localization becomes more challenging with the presence of common pathological variations which could alter its overall appearance. This paper presents a novel OD localization method by incorporating salient visual cues of retinal vasculature: (1) global vessel symmetry, (2) vessel component count and (3) local vessel symmetry inside OD region. In the proposed method, a new vessel symmetry line (VSL) measure is designed to demarcate the lines that divide the retinal vasculature into approximately similar halves. The initial OD center location is computed using the highest number of major blood vessel components in the skeleton image. The final OD center localization involves an iterative center of mass computation to exploit the local vessel symmetry in the OD region of interest. The proposed method shows effectiveness in diseased retinas having diverse symptoms like bright lesions, hemorrhages, and tortuous vessels that create potential ambiguity for OD localization. A total of ten publicly available retinal image databases are considered for extensive evaluation of the proposed method. The experimental results demonstrate high average OD detection accuracy of 99.49%, while achieving state-of-the-art OD localization error in all databases.

12

New Binary Hausdorff Symmetry measure based seeded region growing for retinal vessel segmentation

Panda R., Puhan N. B., Panda G.

Biocybernetics and Biomedical Engineering

|

2016

|

Vol. 36, no. 1

119--129

EN

Automated retinal vessel segmentation plays an important role in computer-aided diagnosis of serious diseases such as glaucoma and diabetic retinopathy. This paper contributes, (1) new Binary Hausdorff Symmetry (BHS) measure based automatic seed selection, and (2) new edge distance seeded region growing (EDSRG) algorithm for retinal vessel segmentation. The proposed BHS measure directly provides a binary symmetry decision at each pixel without the computation of continuous symmetry map and image thresholding. In a multiscale mask, the BHS measure is computed using the distance sets of opposite direction angle bins with sub-pixel resolution. The computation of the BHS measure from the Hausdorff distance sets involves point set matching based geometrical interpretation of symmetry. Then, we design a new edge distance seeded region growing (EDSRG) algorithm with the acquired seeds. The performance evaluation in terms of sensitivity, specificity and accuracy is done on the publicly available DRIVE, STARE and HRF databases. The proposed method is found to achieve state-of-the-art vessel segmentation accuracy in three retinal databases; DRIVE- sensitivity (0.7337), specificity (0.9752), accuracy (0.9539); STARE-sensitivity (0.8403), specificity (0.9547), accuracy (0.9424); and HRF-sensitivity (0.8159), specificity (0.9525), accuracy (0.9420).

13

Computerized screening of diabetic retinopathy employing blood vessel segmentation in retinal images

Franklin S. W., Rajan S. E.

Biocybernetics and Biomedical Engineering

|

2014

|

Vol. 34, no. 2

117--124

EN

Diabetic retinopathy is a severe sight threatening disease which causes blindness among working age people. This research work presents a retinal vessel segmentation technique, which can be used in computer based retinal image analysis. This proposed method could be used as a prescreening system for the early detection of diabetic retinopathy. The algorithm implemented in this work can be effectively used for detection and analysis of vascular structures in retinal images. The retinal blood vessel morphology helps to classify the severity and identify the successive stages of a number of diseases. The changes in retinal vessel diameter are one of the symptoms for diseases based on vascular pathology. The size of typical retinal vessel is a few pixels wide and it becomes critical and challenging to obtain precise measurements using computer based automatic analysis of retinal images. This method classifies each image pixel as vessel or non-vessel and thereby produces the segmentation of vasculature in retinal images. Retinal blood vessels are identified and segmented by making use of a multilayer perceptron neural network, for which the inputs are derived from three primary colour components of the image, i.e., red, green and blue. Back propagation algorithm which provides a proficient technique to change the weights in a feed-forward network is employed. The performance of this method was evaluated and tested using the retinal images from the DRIVE database and has obtained illustrative results. The measured accuracy of the proposed system was 95.03% for the segmentation algorithm tested on this database.

14

Zaburzenia widzenia u osób chorych na cukrzycę typu I: zmiany wrażliwości siatkówki na bodziec świetlny u chorych na cukrzycę typu I – szczegółowa analiza danych perymetrycznych

Brenk J., Szuba R., Schlaffke J., Wierusz-Wysocka B., Tomczak P.

Optyka

|

2013

|

Nr 1

42--46

PL

Zaburzenia w układzie wzrokowym chorych na cukrzycę typu I są wywołane przez nieprawidłowe wartości glikemii oraz zakłóconą gospodarkę metaboliczną. Odchylenia w stężeniach glukozy we krwi są przyczyną zmian refrakcji oka. Mogą też wpływać na sensoryczne funkcje układu wzrokowego (widzenie barwne, poczucie kontrastu, pole widzenia). Ponadto niewyrównana glikemia skutkuje późnymi powikłaniami, np. retinopatią cukrzycową. Jednym z celów specjalistów zajmujących się ochroną zdrowia narządu wzroku u chorych na cukrzycę jest doskonalenie metod wczesnej diagnozy zmian cukrzycowych. Progowa perymetria statyczna jest użyteczną metodą badania wrażliwości siatkówki na bodziec świetlny. Pozwala ona określić granicę rozpoznawalności punktu świetlnego o danej luminancji w określonych kierunkach pola widzenia. Ponadto założyć można, iż badania te, powtórzone po określonym czasie, mogą informować o stabilności odbioru bodźców przez układ wzrokowy.

EN

Dysfunctions in the visual system of patients with type 1 diabetes mellitus (DM 1) are caused by abnormal levels of blood glucose and abnormal metabolic economy. Fluctuations in the blood glucose level cause changes in the refraction error of the eye. It may also affect the sensory function of the visual system (color vision, contrast sensitivity, visual field). In addition, instability in blood glucose levels cause further consequences, such as diabetic retinopathy. One of the main aims of eye healthcare professionals who work with diabetics is to improve early diagnostic methods of diabetic changes. Static threshold perimetry is a useful method for testing of the retina sensitivity to the light stimuli. These measurements allow for determining the lowest luminance which the patients are able to reach as a threshold value in certain directions of the visual field. In addition, threshold perimetry repeated in a given time can indicate the stability of the reception of stimuli by the visual system.

15

Pacjent z cukrzycą w gabinecie kontaktologicznym

Kropacz S.

Optyka

|

2013

|

Nr 1

38--39

PL

Literatura polskojęzyczna. Zarówno w książkach na temat aplikacji soczewek kontaktowych, jak również w pozycjach z zakresu optometrii czy okulistyki (zawierających rozdział na temat aplikacji soczewek kontaktowych) wydanych w języku polskim, właściwie nie ma dokładnych informacji o przeciwwskazaniach do noszenia soczewek kontaktowych przez pacjentów z cukrzycą. Na siedem książek o takiej tematyce, w dwóch trudno znaleźć jakąkolwiek informację na ten temat [1,2].

16

Cukrzycowe powikłania w układzie wzrokowym

Styszyński A.

Optyka

|

2013

|

Nr 1

34--36

PL

Cukrzyca jest genetycznie uwarunkowanym zaburzeniem przemiany węglowodanowej powodowanym względnym lub bezwzględnym niedoborem insuliny. Insulina to hormon wydzielany przez trzustkę. Działanie insuliny polega na: obniżeniu poziomu glukozy we krwi poprzez jej spalanie w tkankach, magazynowaniu glukozy w postaci glikogenu w wątrobie i mięśniach, zwiększeniu syntezy tłuszczów z węglowodanów.

17

Automatic detection of exudates from fundus eye images based on mathematical morphology for diabetic retinopathy monitoring

Stąpor K., Świtoński A.

Studia Informatica

|

2005

|

Vol. 26, nr 1

5-14

EN

In this paper the method for automatic segmentation of exudates from fundus eye images is proposed. The method is composed of the following steps: 1) preprocessing, 2) finding marker image and 3) geodesic reconstraction. The mean sensitivity is 95%.

PL

W artykule przedstawiono metodę segmentacji wysięków na cyfrowych obrazach dna oka. Metoda składa się z następujących kroków: 1) przetwarzanie wstępne, 2) znajdowanie obrazu znaczników, 3) rekonstrukcja geodezyjna. Średnia czułość metody wynosi 95%.

18

Automatic detection of early symptoms of diabetic retinopathy from fundus eye images using mathematical morphology

Stąpor K., Świtoński A.

Studia Informatica

|

2004

|

Vol. 25, nr 3

29-39

EN

In this paper the new method for automatic segmentation of microaneurysms from fundus eye images is proposed. It relies on methods from mathematical grayscale morphology. The new HitAndMiss transformation has been defined forthe detection of markers of watershed transformation.

PL

W artykule przedstawiono nową metodę automatycznej segmentacji mikroaneuryzmatów na cyfrowych obrazach dna oka. Zaproponowana metoda F wykorzystuje narzędzia wieloodcieniowej morfologii matematycznej. Zdefiniowano |: nowe przekształcenie trafi-nie-trafi dla detekcji markerów transformaty wododziało-i wej.

19

Neural network and fuzzy logic for analysis of eye-bottom vasculature

Łubkowski P., Lewenstein K., Chojnacki M.

Elektronika : konstrukcje, technologie, zastosowania

|

2004

|

Vol. 45, nr 8-9

96-98

EN

In the paper we're presenting the results of our work on use of neural networks and fuzzy logic for analysis such eye-bottom images. We propose the methods of analysis of vasculature parameters and the automatic algorithm for detection of the mikroarteries. In this case the process of segmentation, binarization and Fourier transformation on the image was described as well as the influence of parameters of Fourier spectrum on obtained results. Finally we have got correct detection of microarteries: 75% for Fahlmans and perception-type neural network and 80% for fuzzy logic.

PL

W pracy zaprezentowane są wyniki badań nad komputerowa analizą obrazów sieci naczyniowej dna oka wykorzystującą systemy z sieciami neuronowymi i logiką rozmytą. Zaproponowano metody analizy parametrów geometrycznych naczyń oraz działający w oparciu o 2-wymiarową transformację Fouriera system detekcji mikrotętniaków.