The topological derivative (TD) for shape analysis has been employed in image segmentation, and machine learning schames based on convolutional neural network (CNN) provide the high performance in the image processing. The supervised and unsupervised approaches have different roles and advantages according to their concepts. To maximize the benefits of two approaches, we propose CNN-TD based segmentation approach. A CNN-based segmentation scheme is employed to faithfully consider the characteristics of an object to be segmented in a given image, and we refine the CNN results using a TD-based scheme. Experimental results show that the proposed scheme produces better performance for the prostate segmentation than the refined results by level set-based schemes. Therefore, we believe that the proposed scheme can be a useful tool for effective medical image segmentation.

Image smoothing has been used for image segmentation, image reconstruction, object classification, and 3D content generation. Several smoothing approaches have been used at the pre-processing step to retain the critical edge, while removing noise and small details. However, they have limited performance, especially in removing small details and smoothing discrete regions. Therefore, to provide fast and accurate smoothing, we propose an effective scheme that uses a weighted combination of the gradient, Laplacian, and diagonal derivatives of a smoothed image. In addition, to reduce computational complexity, we designed and implemented a parallel processing structure for the proposed scheme on a graphics processing unit (GPU). For an objective evaluation of the smoothing performance, the images were linearly quantized into several layers to generate experimental images, and the quantized images were smoothed using several methods for reconstructing the smoothly changed shape and intensity of the original image. Experimental results showed that the proposed scheme has higher objective scores and better successful smoothing performance than similar schemes, while preserving and removing critical and trivial details, respectively. For computational complexity, the proposed smoothing scheme running on a GPU provided 18 and 16 times lower complexity than the proposed smoothing scheme running on a CPU and the L0-based smoothing scheme, respectively. In addition, a simple noise reduction test was conducted to show the characteristics of the proposed approach; it reported that the presented algorithm outperforms the state-of-the art algorithms by more than 5.4 dB. Therefore, we believe that the proposed scheme can be a useful tool for efficient image smoothing.

Topological derivative has been employed for image segmentation and restoration. The topological derivative-based segmentation uses two sparse matrices, and the computational complexity of the segmentation grows up dramatically as the image size increases due to the size of the sparse matrix. Therefore, to provide a fast and accurate segmentation with low complexity, an effective scheme is proposed with keeping the same segmentation performance. To further reduce the computational complexity, the parallel processing structure for the proposed scheme is designed and implemented on graphics processing unit (GPU). In particular, to reduce the computational cost of generating and multiplying sparse matrices that are squared symmetric, the 2D filters consisting of the coefficients at nonborder regions of sparse matrices are defined, and the multiplication is converted into a convolution filtering. In addition, to design a parallel processing for the segmentation with the proposed scheme on a GPU, an image is divided into several blocks and they are processed in parallel. Experimental results show that the proposed scheme for topological derivative-based segmentation reduces the computational complexity ~ 908 times, and the complexity of the proposed scheme is reduced ~ 17 times more from the parallel structure. In particular, the higher efficiency can be obtained from large sized images because the complexity of the proposed scheme does not depend on the image size. Moreover, the proposed scheme can provide almost identical segmentation result with the original sparse matrix-based approach. Therefore, we believe that the proposed scheme can be a useful tool for efficient topological derivative-based segmentation.