Recently, the remote gaze estimation (RGE) technique has been widely applied to consumer devices as a more natural interface. In general, the conventional RGE method estimates a user’s point of gaze using a geometric transform, which represents the relationship between several infrared (IR) light sources and their corresponding corneal reflections (CRs) in the eye image. Among various methods, the homography normalization (HN) method achieves state-of-the-art performance. However, the geometric transform of the HN method requiring four CRs is infeasible for the case when fewer than four CRs are available. To solve this problem, this paper proposes a new RGE method based on three alternative geometric transforms, which are adaptive to the number of CRs. Unlike the HN method, the proposed method not only can operate with two or three CRs, but can also provide superior accuracy. To further enhance the performance, an effective error correction method is also proposed. By combining the introduced transforms with the error-correction method, the proposed method not only provides high accuracy and robustness for gaze estimation, but also allows for a more flexible system setup with a different number of IR light sources. Experimental results demonstrate the effectiveness of the proposed method.