Various methods have been used to estimate the pupil location within an image or a real-time video frame in many fields. However, these methods lack the performance specifically in low-resolution images and varying background conditions. We propose a coarse-to-fine pupil localisation method using a composite of machine learning and image processing algorithms. First, a pre-trained model is employed for the facial landmark identification to extract the desired eye frames within the input image. Then, we use multi-stage convolution to find the optimal horizontal and vertical coordinates of the pupil within the identified eye frames. For this purpose, we define an adaptive kernel to deal with the varying resolution and size of input images. Furthermore, a dynamic threshold is calculated recursively for reliable identification of the best-matched candidate. We evaluated our method using various statistical and standard metrics along with a standardised distance metric that we introduce for the first time in this study. The proposed method outperforms previous works in terms of accuracy and reliability when benchmarked on multiple standard datasets. The work has diverse artificial intelligence and industrial applications including human computer interfaces, emotion recognition, psychological profiling, healthcare, and automated deception detection.