Image enhancement plays a crucial role in infant fingerprint matching, as child-specific characteristics such as smaller finger dimensions and thinner ridge structures often degrade image quality during acquisition. To address these limitations, enrollment typically depends on specialized highresolution scanners, which most existing enhancement methods are not designed to support. Consequently, identification rates for children remain significantly lower than those achieved with adult fingerprints. This study introduces Recursive Class Connectivity Classification (R3C), a novel framework that iteratively refines binary segmentation outputs from existing enhancement methods by extending ridge structures. R3C does not require modifications to the underlying classifier and operates without training data, which is not currently available for infant fingerprints. Instead, the method improves segmentation by repeatedly feeding the classified image back into the classification process, while combining each intermediate segmentation with the original input image. Experiments conducted on three fingerprint datasets using four different enhancement classifiers show that R3C can increase the True Acceptance Rate (TAR) by up to 4% for children and over 40% for newborns, compared to using the enhancement methods alone. A qualitative analysis further demonstrates that R3C reconnects fragmented ridge patterns, improving the visual quality of segmentation. Because it functions independently of the enhancement method used, R3C provides a flexible and broadly applicable solution for improving binary segmentation.