Other

– Neural Edge Enhancer for Supervised Edge Enhancement from Noisy Images

– Analysis of the Neural Edge Enhancer Trained for Edge Enhancement in Noisy Images

– Reduction of Noise from Images by Use of a Neural Filter

– A Method for Designing the Optimal Structure of a Neural Filter

– Efficient Approximation of Neural Filters for Removing Quantum Noise from Images

– Determining the Receptive Field of a Neural Filter

– Linear-Time Connected-Component Labeling Based on Sequential Local Operations

Neural Edge Enhancer for Supervised Edge Enhancement from Noisy Images

We propose a new edge enhancer based on a modified multilayer neural network, which is called a “neural edge enhancer” (NEE), for enhancing the desired edges clearly from noisy images. The NEE is a supervised edge enhancer: through training with a set of input noisy images and teaching edges, the NEE acquires the function of a desired edge enhancer. The input images are synthesized from noiseless images by addition of noise. The teaching edge images are made from the noiseless images by performing the desired edge enhancer. To investigate the performance, we carried out experiments to enhance edges from noisy artificial and natural images. By comparison with conventional edge enhancers, the following was demonstrated: the NEE was robust against noise, was able to enhance continuous edges from noisy images, and was superior to the conventional edge enhancers in terms of the similarity to the desired edges. Furthermore, we have proposed a method for edge localization for the NEE. We compared the NEE, together with the proposed edge localization method, with a leading edge detector. The NEE was proved to be useful for enhancing edges from noisy images.

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Noisy input image (left) and an ideal edge image (right).

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Sobel edge enhancer (left) and Marr-Hildreth edge enhancer (right).

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Huckel edge enhancer (left) and neural edge enhancer (right).
Comparison of the performance of the trained neural edge enhancer for a non-training image with that of conventional edge enhancers.

Analysis of the Neural Edge Enhancer Trained for Edge Enhancement in Noisy Images

In order to gain insight into the internal presentation of a trained neural edge enhancer, we developed an analysis method for the nonlinear kernel of a trained neural edge enhancer. We trained a neural edge enhancer to enhance edges in noisy images. Our analysis method was applied to the trained neural edge enhancer with a five-by-five-pixel input kernel. Six graphs obtained by the analysis, which correspond to six networks connected to six units in the hidden layer, are shown in the adjacent figure. Because one unit in the hidden layer corresponds to one feature, each network that is connected to a unit in the hidden layer can be shown separately. The five-by-five matrices correspond to the input region of the trained NEE. The black squares indicate pixels having a negative weight. The pixels having the same sign correspond to a smoothing operation, whereas the pixels having the opposite sign correspond to an edge-enhancement operation. The results suggested that the trained neural edge enhancer acquired directional gradient operators with smoothing. These directional gradient operators with smoothing, followed by integration with nonlinearity, lead to robust enhancement of the NEE against noise. It is interesting to note that the result is reminiscent of the receptive fields of various simple units in the cat and monkey cerebral cortex discovered by Hubel and Wiesel in 1968. With the cat and monkey, these neural filters are acquired during the critical period just after birth. Thus, the trained neural filter was able to be analyzed by use of our analysis method, and we found an interesting similarity between an artificial neural edge enhancer and the receptive fields of biological neural filters in the human visual system.

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Six graphs obtained by the analysis of a trained neural edge enhancer which correspond to six networks connected to six units in the hidden layer.

Reduction of Noise from Images by Use of a Neural Filter

The conventional noise-reduction filters tend to blur the edge information while noise is reduced. To address this issue, we developed a supervised nonlinear filter based on an artificial neural network (ANN), called a “neural filter,” for reduction of noise in images. The neural filter is trained with input images and the corresponding teaching images. To reduce noise in images, we created noisy images from original noiseless images by adding noise. We used the noisy images as the input images and the corresponding noiseless images as the teaching images for the neural filter. After training, the neural filter provided images with less noise when it was applied to non-training noisy images. The noise in the input images was reduced while the edge information was maintained. Thus, the neural filter would be useful for reduction of noise in images.

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The input noisy images (left) and the output images of the trained neural filter (right).