Specialists mostly assess the skeletal maturity of short-height children by observing their left hand X-Ray image (radiograph), whereas precise separation of areas capturing the bones and growing plates is always not possible by visual inspection. Although a few attempts are made to estimate a suitable threshold for segmenting digitized radiograph images, their results are not still promising. To finely estimate segmentation thresholds, this paper presents the quantumized genetic algorithm (QGA) that is the integration of quantum representation scheme in the basic genetic algorithm (GA). This hybridization between quantum inspired computing and GA has led to an efficient hybrid framework that achieves better balance between the exploration and the exploitation capabilities. To assess the performance of the proposed quantitative bone maturity assessment framework, we have collected an exclusive dataset including 65 left-hand digitized images, aged from 3 to 13 years. Thresholds are estimated by the proposed method and the results are compared to harmony search algorithm (HSA), particle swarm optimization (PSO), quantumized PSO and standard GA. In addition, for more comparison of the proposed method and the other mentioned evolutionary algorithms, ten known benchmarks of complex functions are considered for optimization task. Our results in both segmentation and optimization tasks show that QGA and GA provide the best optimization results in comparison with the other mentioned algorithms. Moreover, the empirical results demonstrate that QGA is able to provide better diversity than that of GA.