Grayscale logo watermarking is a quite well-developed area of digital image watermarking which seeks to embed into the host image another smaller logo image. The key advantage of such an approach is the ability to visually analyze the extracted logo for rapid visual authentication and other visual tasks. However, logos pose new challenges for invisible watermarking applications which need to keep the watermark imperceptible within the host image while simultaneously maintaining robustness to attacks. This paper presents an algorithm for invisible grayscale logo watermarking that operates via adaptive texturization of the logo. The central idea of our approach is to recast the watermarking task into a texture similarity task. We first separate the host image into sufficiently textured and poorly textured regions. Next, for textured regions, we transform the logo into a visually similar texture via the Arnold transform and one lossless rotation; whereas for poorly textured regions, we use only a lossless rotation. The iteration for the Arnold transform and the angle of lossless rotation are determined by a model of visual texture similarity. Finally, for each region, we embed the transformed logo into that region via a standard wavelet-based embedding scheme. We employ a multistep extraction stage, in which an affine parameter estimation is first performed to compensate for possible geometrical transformations. Testing with multiple logos on a database of host images and under a variety of attacks demonstrates that the proposed algorithm yields better overall performance than competing methods.