Antonyms for "taking notice of" include ignoring, disregarding, overlooking, neglecting, and dismissing. When we ignore someone or something, we deliberately choose to turn a blind eye or deaf ear to it, while disregarding suggests a lack of concern or interest. Overlooking implies a failure to observe or take note of something significant, while neglecting suggests a failure to give proper attention or care to something. Finally, dismissing involves rejecting or denying the importance or value of something, and it often implies a level of indifference or arrogance. In short, these antonyms reflect a range of attitudes and behaviors towards paying attention to details or people in our lives.