Color graph based wavelet transform with perceptual information

International audienceIn this paper, we propose a numerical strategy to define a multiscale analysis for color and multicomponent images based on the representation of data on a graph. Our approach consists in computing the graph of an image using the psychovisual information and analysing it by using the spectral graph wavelet transform. We suggest introducing color dimension into the computation of the weights of the graph and using the geodesic distance as a means of distance measurement. We thus have defined a wavelet transform based on a graph with perceptual information by using the CIELab color distance. This new representation is illustrated with denoising and inpainting applications. Overall, by introducing psychovisual information in the graph computation for the graph wavelet transform we obtain very promising results. Therefore results in image restoration highlight the interest of the appropriate use of color information

Realtime image noise reduction FPGA implementation with edge detection

The purpose of this dissertation was to develop and implement, in a Field Programmable Gate Array (FPGA), a noise reduction algorithm for real-time sensor acquired images. A Moving Average filter was chosen due to its fulfillment of a low demanding computational expenditure nature, speed, good precision and low to medium hardware resources utilization. The technique is simple to implement, however, if all pixels are indiscriminately filtered, the result will be a blurry image which is undesirable. Since human eye is more sensitive to contrasts, a technique was introduced to preserve sharp contour transitions which, in the author’s opinion, is the dissertation contribution. Synthetic and real images were tested. Synthetic, composed both with sharp and soft tone transitions, were generated with a developed algorithm, while real images were captured with an 8-kbit (8192 shades) high resolution sensor scaled up to 10 × 103 shades. A least-squares polynomial data smoothing filter, Savitzky-Golay, was used as comparison. It can be adjusted using 3 degrees of freedom ─ the window frame length which varies the filtering relation size between pixels’ neighborhood, the derivative order, which varies the curviness and the polynomial coefficients which change the adaptability of the curve. Moving Average filter only permits one degree of freedom, the window frame length. Tests revealed promising results with 2 and 4ℎ polynomial orders. Higher qualitative results were achieved with Savitzky-Golay’s better signal characteristics preservation, especially at high frequencies. FPGA algorithms were implemented in 64-bit integer registers serving two purposes: increase precision, hence, reducing the error comparatively as if it were done in floating-point registers; accommodate the registers’ growing cumulative multiplications. Results were then compared with MATLAB’s double precision 64-bit floating-point computations to verify the error difference between both. Used comparison parameters were Mean Squared Error, Signalto-Noise Ratio and Similarity coefficient.O objetivo desta dissertação foi desenvolver e implementar, em FPGA, um algoritmo de redução de ruído para imagens adquiridas em tempo real. Optou-se por um filtro de Média Deslizante por não exigir uma elevada complexidade computacional, ser rápido, ter boa precisão e requerer moderada utilização de recursos. A técnica é simples, mas se abordada como filtragem monotónica, o resultado é uma indesejável imagem desfocada. Dado o olho humano ser mais sensível ao contraste, introduziu-se uma técnica para preservar os contornos que, na opinião do autor, é a sua principal contribuição. Utilizaram-se imagens sintéticas e reais nos testes. As sintéticas, compostas por fortes e suaves contrastes foram geradas por um algoritmo desenvolvido. As reais foram capturadas com um sensor de alta resolução de 8-kbit (8192 tons) e escalonadas a 10 × 103 tons. Um filtro com suavização polinomial de mínimos quadrados, SavitzkyGolay, foi usado como comparação. Possui 3 graus de liberdade: o tamanho da janela, que varia o tamanho da relação de filtragem entre os pixels vizinhos; a ordem da derivada, que varia a curvatura do filtro e os coeficientes polinomiais, que variam a adaptabilidade da curva aos pontos a suavizar. O filtro de Média Deslizante é apenas ajustável no tamanho da janela. Os testes revelaram-se promissores nas 2ª e 4ª ordens polinomiais. Obtiveram-se resultados qualitativos com o filtro Savitzky-Golay que detém melhores características na preservação do sinal, especialmente em altas frequências. Os algoritmos em FPGA foram implementados em registos de vírgula fixa de 64-bits, servindo dois propósitos: aumentar a precisão, reduzindo o erro comparativamente ao terem sido em vírgula flutuante; acomodar o efeito cumulativo das multiplicações. Os resultados foram comparados com os cálculos de 64-bits obtidos pelo MATLAB para verificar a diferença de erro entre ambos. Os parâmetros de medida foram MSE, SNR e coeficiente de Semelhança