IEEE TRANS. VISUALIZATION AND COMPUTER GRAPHICS, VOL. X, NO. Y, ZZZZZ XXXX 1 Bas-Relief Generation Using Adaptive Histogram Equalisation Xianfang Sun, Paul L. Rosin, Ralph R. Martin, and Frank C. Langbein, Member, IEEE Abstract—An algorithm is presented to automatically generate bas-reliefs based on adaptive histogram equalisation (AHE), starting from an input height field. A mesh model may al- ternatively be provided, in which case a height field is first created via orthogonal or perspective projection. The height field is regularly gridded and treated as an image, enabling a modified AHE method to be used to generate a bas-relief with a user-chosen height range. We modify the original image- contrast-enhancement AHE method to also use gradient weights, to enhance the shape features of the bas-relief. To effectively compress the height field, we limit the height-dependent scaling factors used to compute relative height variations in the output from height variations in the input; this prevents any height differences from having too great an effect. Results of AHE over different neighbourhood sizes are averaged to preserve informa- tion at different scales in the resulting bas-relief. Compared to previous approaches, the proposed algorithm is simple and yet largely preserves original shape features. Experiments show that our results are in general comparable to and in some cases better than the best previously published methods. Index Terms—Bas-relief, adaptive histogram equalisation, fea- ture enhancement. I. I NTRODUCTION Bas-relief sculpting is a technique which has been practised for thousands of years. The idea is straightforward: a flattened sculpture is produced on some base surface—for example, por- traiture on coinage. The overall range of depth of the elements in the sculpture is highly compressed. Parallel or perspective viewing effects may also be used. Bas-reliefs usually have a single z depth for each x-y position, and portions of the scene nearest to the viewer are elevated most [1]. The production of bas-reliefs is currently a costly and time- consuming process, requiring skilled sculptors and engravers. Automatic capture of computer models of 3D shape is be- coming more commonplace using 3D scanners. This provides a foundation for automation in bas-relief making, resulting in reduced costs, and shorter time-to-market. Such advantages also allow bas-reliefs to be extended to a wider range of application areas such as packaging, where traditionally the costs or lead times have often been too high. However, current commercial CAD tools for bas-relief work, such as Delcam’s ArtCAM, cannot yet be considered to provide a full solution to relief making. X. Sun is with the School of Computer Science, Cardiff University, 5 The Parade, Cardiff CF24 3AA, UK, and the School of Automation Science and Electrical Engineering, Beihang University, Beijing 100191, P. R. China. E- mail: Xianfang.Sun@cs.cardiff.ac.uk. P. L. Rosin, R. R. Martin, and F. C. Langbein are with the School of Computer Science, Cardiff University, 5 The Parade, Cardiff CF24 3AA, UK. E-mail: {Paul.Rosin, Ralph.Martin, F.C.Langbein}@cs.cardiff.ac.uk. Manuscript received XXXX. Of course, considerable artistic skills are needed to decide upon the composition and view of the subject matter. Having chosen these, however, simple experimentation shows that an acceptable bas-relief cannot be made by linearly compressing a 3D scene’s depth coordinates while preserving width and height (see Fig. 1(b)). In principle, by suitably choosing the direction of the light source, and the surface albedo, the image of a bas-relief generated by an affine transformation of the 3D surface can be indistinguishable from that of the original 3D surface [2]. However, in most cases, it is not possible to control the light source, surface albedo and viewpoint. Considerably more sophisticated methods are needed to produce a bas-relief which has the right kind of visual appearance [3]–[6]. The academic work to date has considered the issue of how to achieve the necessary compression of depths, and even so, has not achieved entirely satisfactory results. The next section summarises state-of-the-art approaches. We then present a new depth compression method based on an adaptive histogram equalisation (AHE) method taken from image processing, which has been adapted to bas-relief pro- duction. Our goal is a simple method for bas-relief generation which clearly preserves visible shape details in the final results, as demonstrated in Fig. 1(c). II. PREVIOUS WORK Relatively little academic literature to date has considered the automatic production of bas-reliefs. One older paper [1] gives a basic approach to the problem, while two recently published papers independently devised rather similar, more sophisticated, solutions [4], [6]. The earliest paper [1] treats bas-relief generation as a prob- lem of embossing on the view plane. The key principle used is that depth within the relief should be a function of the distance between the observer and any projected point. The authors expect this function to preserve linearity, and note that standard perspective transformation has the required properties. Thus, they compress z coordinates inversely with distance, while also adding perspective in x and y if desired. Their results are generally of the correct nature, but of unacceptable quality in detail. For example, a bas-relief of a head gives undue prominence to the hair, while other reliefs may look rather flat. The authors note that good results can only be obtained if the artist subtly edits the 3D model before applying their approach. However, they state an important principle for generating bas- reliefs: unused depth intervals at height discontinuities should be removed (either manually or automatically) to make best use of the allowed bas-relief depth.