In pictures, every object is displayed in 2D space. Seeing the 2D image, people can perceptually reconstruct and understand information regarding the scene. To enable users to haptically interact with an object that appears in the image, the present study proposes a geometry-based haptic rendering method. More specifically, our approach is intended to estimate haptic information from the object's structure contained in an image while preserving the two-dimensional visual information. Of the many types of objects that can be seen in everyday pictures, this paper mainly deals with polyhedron figures or objects composed of rectangular faces, some of which might be shown in a slanted configuration in the picture. To obtain the geometric layout of the object being viewed from the image plane, we first estimate homographic information that describes a mapping from the object coordinate to the target image coordinate. Then, we transform the surface normals of the object face using the extrinsic part of homography that locates the face of the object we are viewing. Because the transformed normals are utilized for calculating the force in the image space, we call this process normal vector perturbation in the 2D image space. To physically represent the estimated normal vector without distorting the visual information, we employed a lateral haptic rendering scheme in that it fits with our interaction styles on 2D images. The active force value at a given position on the slanted faces is calculated during the interaction phase. To evaluate our approach, we conducted an experiment with different stimulus conditions, in which it was found that participants could reliably estimate the geometric layout that appears in the picture. We conclude with explorations of applications and a discussion of future work.