This paper presents a new approach for reconstruction of disconnected digital lines (DDLs) based on a constrained regularization model which ensures connectivity of the digital lines (DLs) in the discrete image plane. The first step in this approach is to determine the order of given pixels of the DDL. To determine connectivity of pixels, we use the usual 8-neighbor connectivity in discrete images. For any neighboring pixels of the DDL that are not connected, we determine a number of new pixel values that need to be reconstructed between these pixels. Next, the integer-valued $x$ - and $y$ -coordinates of the location of the pixels of the DDLs are segregated into two 1D signal vectors. Then the $x$ - and $y$ -coordinates of the missing pixels of the DDLs are estimated using a new constrained regularization. While the solution of this constrained minimization problem provides real values for the $x$ - and $y$ -coordinates of pixels positions, the imposed constraint ensures connectivity of the resulting DLs in the image plane after transforming the computed values from $\mathbb {R}$ to $\mathbb {N}$ . The proposed regularization approach forces connected lines with small curvature. The experimental results demonstrate that the proposed technique improves DL intersection detection, as well. Moreover, this technique has a high potential to be used as a fast approach in binary image inpainting particularly overcoming the shortcomings of conventional methods which cause destruction of thin objects and blurring in the recovered regions.

中文翻译：

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基于约束正则化的连通数字线路重构

本文提出了一种基于约束正则化模型的断开数字线 (DDL) 重建的新方法，该模型确保离散图像平面中数字线 (DL) 的连通性。这种方法的第一步是确定 DDL 的给定像素的顺序。为了确定像素的连通性，我们在离散图像中使用通常的 8-neighbor 连通性。对于 DDL 的任何未连接的相邻像素，我们确定需要在这些像素之间重建的许多新像素值。接下来，整数值 $x$ - 和 $y$ -DDL 的像素位置坐标被分成两个 1D 信号向量。然后 $x$ - 和 $y$ - 使用新的约束正则化估计 DDL 缺失像素的坐标。虽然这个约束最小化问题的解决方案为 $x$ - 和 $y$ - 像素位置的坐标，施加的约束确保在将计算值从 $\mathbb {R}$至 $\mathbb {N}$ . 所提出的正则化方法强制连接具有小曲率的线。实验结果表明，所提出的技术也改进了 DL 交叉点检测。此外，该技术具有很高的潜力，可用作二值图像修复的快速方法，特别是克服了传统方法导致薄物体破坏和恢复区域模糊的缺点。