Recently, deep neural networks have been widely used to approximate or improve image operators. In general, an image operator has some hyper-parameters that change its operating configurations, e.g., the strength of smoothing, up-scale factors in super-resolution, or a type of image operator. To address varying parameter settings, an image operator taking such parameters as its input, namely a parameterized image operator, is an essential cue in image processing. Since many types of parameterization techniques exist, a comparative analysis is required in the context of image processing. In this paper, we therefore analytically explore the operation principles of these parameterization techniques and study their differences. In addition, performance comparisons between image operators parameterized by using these methods are assessed experimentally on common image processing tasks including image smoothing, denoising, deblocking, and super-resolution.