<p>Secret image sharing (SIS) possesses advantageous attributes such as loss tolerance, offering a promising solution for image protection. However, the issue remains unresolved, which is the trade-off between the transmission or storage overhead of shadow images and the concealment of secret distribution. This paper designs a novel polynomial splitting framework and proposes the first SIS scheme with multi-sized shadow images. By splitting the original polynomial into various levels containing different numbers of sub-polynomials, the proposed scheme enables the generation of multi-sized shadow images. Moreover, since polynomial splitting is compatible with image bit-plane decomposition, we introduce the first progressive secret image sharing scheme with multi-sized shadow images (PSIS-MS). The secret image can be recovered by integrating multi-sized shadow images, with the visual fidelity of the recovered image progressively enhancing as the quantity of shadow images increases. The proposed schemes generate multi-sized shadow images with an average size smaller than the original image, reducing communication overhead and enhancing the concealment of secret distribution. Theoretical analysis and experimental comparison demonstrate the validity of the proposed schemes.</p>