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We propose a regularized semiparametric mixture cure-rate model for high-dimensional imaging predictors that separates susceptibility to AD conversion from time to AD among susceptible subjects. Baseline MRI images are represented by bivariate Bernstein spline basis functions over a triangulation of the brain domain, and sparsity-inducing penalties are imposed on imaging effects in both incidence and latency components. This construction enables direct estimation of localized coefficient functions describing how image regions are associated with susceptibility and conversion time. We develop an expectation\u2014maximization algorithm that updates latent susceptibility probabilities and solves penalized logistic and Cox regression subproblems, together with an efficient tuning strategy. Simulations show that the method can recover localized active regions and provide useful incidence and latency discrimination. 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