Reconstruction of Connected Digital Lines Based on Constrained Regularization

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.