This thesis presents the research, development and testing of a framework for the data processing of a new approach to the inspection of deep vertical mine shafts. The new approach enables an uninterrupted mining operation while simultaneously providing a continuous photographic documentation of the entire shaft through the use of Hyper Resolution Image Mosaics (HRIM), i.e. images with upwards of 107 pixels. The algebraic and computational framework presented in this thesis is capable of producing HRIM, independent of the size of the observed structure, enabling a remote inspection of its surface. The framework presented in this thesis is specifically suited for the monitoring of active shafts since the data acquisition does not interrupt the shaft operation. Furthermore the framework foregoes the need of experts for the data processing. Additionally the computational implementation of the framework was designed and tested to scale with the computer hardware and take advantage of server structures if they are available to reduce computation time. The aim of this approach is to provide a comparative inspection tool, however it does not provide a metric representation which allows for absolute measurements. The algebraic framework involves the alignment, geometric mapping, blending and tiling of the separate images of the observed structure, to form a HRIM. Data sets collected during a measurement campaign in an underground mine in Sweden, as well as simulated data sets are used to verify the computational implementation of the algebraic framework. The tools developed and presented in this thesis were successfully verified and tested on a data set containing 70000 files, images and their metadata, acquired in a 103 m deep vertical mine shaft. They enable a remote visual inspection of vertical deep mine shafts in a self contained, easy to use manner. Potentially reducing the costs associated with mandated visual inspections of vertical deep mine shafts. The use of HRIM for the remote visual inspection of deep vertical mine shafts has been validated by experimental results which are presented in this thesis.