In multi-attribute models in marketing, a consumer’s preference for a brand in a product class is expressed as a weighted sum of the brand’s attribute values. However, marketing is abundant with examples where two brands may have approximately the same attribute values but enjoy very different market shares, e.g., Coke and Pepsi may have the same values for “sweetness,” “carbonation,” and “price” but have quite different market shares; two political candidates may take approximately the same position on relevant political issues but enjoy different levels of voter support. Defining “image” to be the component of preference not explained by the attributes used in the multi-attribute model, the aim is to empirically estimate the “images” for the different brands. It turns out that the estimation problems have a close relationship to some minimum cost network flow problems in Operations Research. An empirical application of the proposed approach to estimate the “images” for different primary health-care physicians in a rural area reveals that the “image” component substantially improves the validity of the multi-attribute model.