Mixed integer ink selection for spectral reproduction

Abstract

We introduce a novel ink selection method for spectral printing. The ink selection algorithm takes a spectral image and a set of inks as input, and selects a subset of those inks that results in optimal spectral reproduction. We put forward an optimization formulation that searches a huge combinatorial space based on mixed integer programming. We show that solving this optimization in the conventional reflectance space is intractable. The main insight of this work is to solve our problem in the spectral absorbance space with a linearized formulation. The proposed ink selection copes with large-size problems for which previous methods are hopeless. We demonstrate the effectiveness of our method in a concrete setting by lifelike reproduction of handmade paintings. For a successful spectral reproduction of high-resolution paintings, we explore their spectral absorbance estimation, efficient coreset representation, and accurate data-driven reproduction.

Mixed Integer Neural Inverse Design

“…For our analyses and experiments, we focus on real-life applications in neural spectral printing [Shi et al 2018;Ansari et al 2020] and photonic design [Peurifoy et al 2018;Nadell et al 2019]. We solve all MILPs using Gurobi, a state-of-the-art solver [Gurobi Optimization 2018].…”

“…A particularly interesting related work is the recent ink selection method [Ansari et al 2020]. In order to benefit from MILP solvers, for the ink selection problem, this work develops a linear, but approximate forward model that predicts the spectra of different ink combinations.…”

“…In this experiment we used two different neural networks as the input to our method. The 4-ink network is a trained PL-NSM with 4 hidden layers each having 100 neurons and ReLU activation functions [Ansari et al 2020]. The 44-ink network is a trained PL-NSM with 2 hidden layers each having 50 neurons and ReLU activation functions.…”

“…Here the inverse design problem, known as spectral separation, concerns finding the ink ratios for a target spectrum. A particularly challenging target for spectral separation is the perfect gray ramp introduced by Ansari et al [2020]. This gradient is formed by 901 dark to light ideal gray spectra which have equal reflectively across all visible wavelengths (Figure 2).…”

A gradient-based framework for 3D print appearance optimization

“…1. For this proof-of-concept we show a brute-force search but note that more sophisticated strategies (e.g., Shi et al [2018] and Ansari et al [2020]) could be transferred from the aforementioned fields in the future.…”