HySim: An Efficient Hybrid Similarity Measure for Patch Matching in Image Inpainting

TL;DR

This paper proposes an improved modeldriven approach relying on patch-based techniques, which deviates from the standard Sum of Squared Differences (SSD) similarity measure by introducing a Hybrid Similarity (HySim), which enhances patch selection, leading to high-quality inpainting results with reduced mismatch errors.

Abstract

Inpainting, for filling missing image regions, is a crucial task in various applications, such as medical imaging and remote sensing. Trending data-driven approaches efficiency, for image inpainting, often requires extensive data preprocessing. In this sense, there is still a need for model-driven approaches in case of application constrained with data availability and quality, especially for those related for time series forecasting using image inpainting techniques. This paper proposes an improved modeldriven approach relying on patch-based techniques. Our approach deviates from the standard Sum of Squared Differences (SSD) similarity measure by introducing a Hybrid Similarity (HySim), which combines both strengths of Chebychev and Minkowski distances. This hybridization enhances patch selection, leading to high-quality inpainting results with reduced mismatch errors. Experimental results proved the effectiveness of our approach against other model-driven techniques, such as diffusion or patch-based approaches, showcasing its effectiveness in achieving visually pleasing restorations.

Figures (15)

• Figure 1: Comprehensive Overview of Image Inpainting Approaches.
• Figure 2: Illustration of the diffusion-based inpainting process.$\Phi$ is the source region, $\Omega$ is the target region, $\partial \Omega$ is $\Omega$ boundary.
• Figure 3: Illustration of the patch-based inpainting process.$\Phi$ is the source region, $\Omega$ is the target region, $\partial \Omega$ is $\Omega$ boundary, $\Psi_p$ is the target patch, $\Psi_q$ is the selected patch.
• Figure 4: Notation diagram.$\Phi$ is the source region, $\Omega$ is the target region, $\partial \Omega$ is $\Omega$ boundary, $\Psi_p$ is the target patch, $n_p$ is the normal to the contour $\partial \Omega$, and $\nabla I_p^{\bot }$ is the isophote.
• Figure 5: A visual proof of mismatch error. (a) the original image, (b) the target region, which is marked in white, (c) the first iteration of criminisi2004region, (d)-(g) Different iteration of the inpainting process, (h) the last iteration.

Theorems & Definitions (3)

• Definition 1
• Proposition 1
• proof