The space-time image velocimetry (STIV) method evaluates the velocity of a water surface by analyzing a texture angle within a space-time image (STI) obtained from an image sequence of the flowing water's surface. The brightness gradient tensor (BGT) has been utilized for calculating the texture angle of the STI within the original STIV. The BGT is sensitive to image quality, especially high-frequency noise, and this fact limits the capability and accuracy of the velocity estimation. The objectives of this study were to understand why the BGT is sensitive to high-frequency noise and how to resolve this defect. In the manuscript, derivation of the BGT is first reviewed and then a geometric representation of the BGT is discussed. The reason the BGT is sensitive to high-frequency noise is also discussed, and, then, based on geometric representations of the BGT, a measure to improve this defect is proposed. To demonstrate differences between the two methods, texture angles from artificial and field image sets were also analyzed using the BGT and the improved BGT.