**1. Introduction**

The chapter aims to bridge the gap between AI and Mathematics at core of it. They represent the two branches of the same tree [1]. But since they are taught independently, many times it becomes difficult to connect the two and look at the broader picture with a satellite view. AI was invented way back in 1950's by John Mc Carthy who coined the phrase the science and engineering of making intelligent machines. A brief history could be referred in [2].

The three layers of AI basically consist of Incremental advancements in algorithm design, application to specific design and step change is performed for improvement. Mathematical and statistical concept clarity is highly desirable to understand and

implement AI. At this point, an attempt is made with few topics to show the connection in a lucid way. Few explanations are beyond the scope of the chapter so are stated with detailed references for further explorations.

Since there is a deep connection between mathematics, image processing and forensic sciences, the topics included will be an initial knowhow to start exploring the possibilities to scholars in forensic based image processing. Multimedia forensic utilizes AI techniques which involve convolution neural network. Analysis of forensic image is used to decode the fake information about photographs using machine learning [3], another important application is in medicine for forensic anthropology [4]. To understand such recent research in multimedia, concepts of image sampling, enhancement, convolution and neural network are included in this chapter. IoT based forensic analysis also utilizes the statistical approaches discussed.

Beginning with few basic image processing and mathematical expressions, a systematic development is traced through score-based likelihood used in forensic exploration. It would be beneficial to a reader interested in exploring the quantitative procedure to weigh evidence which would use likelihood ratio [5]. In the later part of the chapter a brief introduction to neural network paving the path to digital forensic neural network is included.

Keeping the above idea in mind, the first section includes a brief discussion on topics of image processing and mathematical representation, image formation model, image sampling, intensity transformation and spatial filtering, image enhancement using Laplacian mask, image denoising, order statistics filters, convolution in image processing. The second section is dedicated to forensic image processing and mathematics which includes widely concepts of steganography, discrete Fourier transform, score-based likelihood, and finally an overview of Neural network and probability theory.
