Enhancement of Cone-Beam Computed Tomography Dental-Maxillofacial Images by Sampling Kantorovich Algorithm

Danilo Costarelli,Marco Seracini,Gianluca Vinti,Pietro Pozzilli

doi:10.3390/sym13081450

Abstract

In this paper, we establish a procedure for the enhancement of cone-beam computed tomography (CBCT) dental-maxillofacial images; this can be useful in order to face the problem of rapid prototyping, i.e., to generate a 3D printable file of a dental prosthesis. In the proposed procedure, a crucial role is played by the so-called sampling Kantorovich (SK) algorithm for the reconstruction and image noise reduction. For the latter algorithm, it has already been shown to be effective in the reconstruction and enhancement of real-world images affected by noise in connection to engineering and biomedical problems. The SK algorithm is given by an optimized implementation of the well-known sampling Kantorovich operators and their approximation properties. A comparison between CBTC images processed by the SK algorithm and other well-known methods of digital image processing known in the literature is also given. We finally remark that the above-treated topic has a strong multidisciplinary nature and involves concrete biomedical applications of mathematics. In this type of research, theoretical and experimental disciplines merge in order to find solutions to real-world problems.

Highlights

We state some new applications of a certain family of approximation operators, known under sampling Kantorovich (SK) operators, which have been deeply studied in recent years in connection to both theoretical and practical aspects.The SK operators have been introduced in [1] in a one-dimensional setting, and subsequently, they have been extended to the multivariate frame in [2]
The new application that we study is related to the reconstruction and the enhancement of dental cone-beam computed tomography (CBCT) images, in connection to the problem of prototyping
We compared the results achieved by bilinear and bicubic algorithms with the ones coming from sampling Kantorovich operators

Summary

Introduction

We state some new applications of a certain family of approximation operators, known under sampling Kantorovich (SK) operators, which have been deeply studied in recent years in connection to both theoretical and practical aspects.The SK operators have been introduced in [1] in a one-dimensional setting, and subsequently, they have been extended to the multivariate frame in [2]. The SK operators (based upon non-negative kernels) belong to the wide family of linear (positive) operators, which is one of the most studied topics in approximation theory (see, e.g., [3,4,5,6,7]). The new application that we study is related to the reconstruction and the enhancement of dental cone-beam computed tomography (CBCT) images (or cone-beam computed tomography, [10,11,12]), in connection to the problem of prototyping. In this regard, a crucial role is played by the SK operators and their implementation for image processing

Methods

Results

Conclusion