Visual sensor network (VSN) requires a multi-focus image or video frame fusion technique involving focus measure computation in the DCT-domain to generate an all-in-focus image. Such techniques are implemented on resource-constrained on-board systems requiring hardware-friendly implementations. In this article, we first show that components of the Laplacian matrix are related to the discrete cosine transform (DCT) basis. The relation is that the eigenvalues of the Laplacian with proper boundary condition form the diagonal elements of the diagonal matrix generated by the DCT operation on the Laplacian. Exploiting this relation, we propose a focus measure which works on the DCT coefficients reflecting the spatial-domain Laplacian operation. Certain simplifications allow our focus measure computation through hardware-friendly integer multiplication and summation, where matrix multiplication involves just N scalar multiplications for an $N\times N~2\text{D}$ signal. Finally, we propose an approach which suitably fuses multi-focus images or video frames in DCT based image or video coding framework through detection of properly focused area and neighborhood consistency analysis. We show that our proposed approach is hardware-friendly, computationally simple, and is fast enough for VSN. Through experimental results, we show that our approach outperforms the relevant state-of-the-art in multi-focus image fusion for VSN both quantitatively and subjectively. We also show that our approach is effective in comparison to the state-of-the-art and a few latest generic multi-focus image fusion techniques in terms of quantitative and subjective evaluations.

中文翻译：

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基于硬件友好拉普拉斯算子的视觉传感器网络DCT域多焦点图像融合

视觉传感器网络 (VSN) 需要多焦点图像或视频帧融合技术，涉及 DCT 域中的焦点测量计算，以生成全焦点图像。这些技术在需要硬件友好实现的资源受限的车载系统上实现。在本文中，我们首先说明拉普拉斯矩阵的分量与离散余弦变换 (DCT) 基有关。关系是具有适当边界条件的拉普拉斯算子的特征值形成对拉普拉斯算子进行 DCT 运算生成的对角矩阵的对角元素。利用这种关系，我们提出了一种聚焦度量，该度量适用于反映空间域拉普拉斯运算的 DCT 系数。某些简化允许我们通过硬件友好的整数乘法和求和来计算焦点度量，其中矩阵乘法仅涉及 $N\times N~2\text{D}$ 信号的 N 个标量乘法。最后，我们提出了一种方法，通过检测正确聚焦的区域和邻域一致性分析，在基于 DCT 的图像或视频编码框架中适当地融合多焦点图像或视频帧。我们表明我们提出的方法对硬件友好，计算简单，并且对于 VSN 来说足够快。通过实验结果，我们表明我们的方法在数量和主观上都优于 VSN 多焦点图像融合的相关最新技术。