Retinal fundus images captured from fundus cameras are widely used by medical professionals for early detection and diagnosis of various ocular and systemic diseases. Over the years, many studies have been conducted for automatic vessel extraction and optic disc (OD) localisation using computers which can be crucial in identifying retinal diseases. In resource-limited situations, the equipment needed to capture and analyse fundus images can be difficult to set up. We developed a smartphone application that uses Bar-Combination of Shifted Filter Response (B-COSFIRE) filter for vessel segmentation and Hough transform with vessel inpainting for OD localisation. The image processing computation is executed in a Python software development kit (SDK) running on the Android platform. The application is designed to perform retinal analysis locally on a mobile device, which includes vessel segmentation and OD localisation. Qualitative and quantitative assessment of this study showed that the method not only achieved comparable performance but also faster on mobile devices than other similar state-of-the-art methods. In the future, the application can be further developed to be used with a handheld fundus camera for a truly mobile retinal analysis system. This can open a potential field for faster, more portable, and more cost-effective retinal image analysis for easier diagnosis.