Normal manipulation for bas-relief modeling

Abstract

We introduce a normal-based modeling framework for bas-relief generation and stylization which is motivated by the recent advancement in this topic. Creating bas-relief from normal images has successfully facilitated bas-relief modeling in image space. However, the use of normal images in previous work is restricted to the cut-and-paste or blending operations of layers. These operations simply treat a normal vector as a pixel of a general color image. This paper is intended to extend normal-based methods by processing the normal image from a geometric perspective. Our method can not only generate a new normal image by combining various frequencies of existing normal images and details transferring, but also build bas-reliefs from a single RGB image and its edge-based sketch lines. In addition, we introduce an auxiliary function to represent a smooth base surface or generate a layered global shape. To integrate above considerations into our framework, we formulate the bas-relief generation as a variational problem which can be solved by a screened Poisson equation. One important advantage of our method is that it can generate more styles than previous methods and thus it expands the bas-relief shape space. We experimented our method on a range of normal images and it compares favorably to other popular classic and state-of-the-art methods.

Introduction

Relief, commonly used for thousands of years, is an art form between drawing and sculpture in which a solid piece of material is carved so that figures emerge from the background. Bas-relief is a type of relief that projects only slightly from the background, but registers as a three-dimensional image when viewed from the front. Even with the development of computer-aided-design, the design of bas-reliefs remains mainly in the hands of artists. Recently, the problem of automatic generation of bas-reliefs from 3D input scenes has received great attention. To simplify the problem, bas-reliefs are usually represented as 2.5D height fields that give each position $(x,y)$ a single depth $z$ above the background. Consequently, the key technique for bas-relief generation is the compression of the height field sampled from the input 3D scenes.

Previous methods on bas-relief generation can be classified into two main categories: gradient-based methods and normal-based methods. Gradient-based methods compress the height field in gradient domain, and reconstruct a new height field by integrating over the modified gradients. One disadvantage of these methods is that the attenuation of height discontinuities relies much on parameter tuning [1]. In contrast, normal-based methods, which compress the height field by preserving surface normals of the input object, are intrinsically detail-preserving and free from height discontinuity.

Before this paper, several normal-based methods have been proposed to generate bas-reliefs, either in image domain [2], [3], or mesh domain [4], [5]. These methods mainly focus on surface normal preserving and details enhancement, but lack of the capability of global shape control of the bas-reliefs and hierarchical editing of the geometrical details. This paper attempts to expand the bas-relief shape space and generates more styles of bas-reliefs. To this end, we introduce a normal filter to extract the normal variation at different scales. The proposed filter is inspired by the Difference of Gaussians (DoG) filter [6]. Similar to the band-pass $DoG$ filter, our filter extracts normal variation through a certain band, which can be used to decompose the normal into different components. The decomposed normal components can be edited, transferred or composed again if necessary. Our method then generates bas-reliefs from the resulting normal image. In addition, a variational formulation with a data fidelity term and a regularization term is proposed to control the global appearance of the resulting bas-relief. The main contributions of this paper are summarized as follows:

Two-scale bas-relief modeling. We propose a two-scale algorithm for bas-relief modeling. In this paper, bas-relief modeling can be achieved from two scales. First, one can create a base normal layer from scratch or based on an existing normal image. This layer describes the global shape on a large scale. Then, a detailed layer is created from an existing normal image or general image. This layer encodes the high-frequency details on a small scale. These two layers are composed to obtain the final normal image. Both layers can be edited respectively, and then one can obtain a series of bas-reliefs.

Shape controlling. To control the global appearance of the resulting bas-relief, we introduce an auxiliary function $h(u,v)$ to represent base surfaces which can include smooth shapes and step-shaped surfaces.

Bas-relief modeling from photographic image. Our algorithm is adapted to produce bas-reliefs from a single photographic image in which the objects are homogeneous (sharing similar materials). Constructing a base layer by use of an edge map extracted from the input photographic image, then building a detail normal layer by use of a grayscale image obtained from the same photographic image, and finally combining them in the normal domain to produce a plausible bas-relief.

This paper is organized as follows: Section 2 describes related work and summarizes state-of-the-art approaches. In Section 3 we give an overview of our algorithm. In Section 4 we introduce a DoG-like filter to extract higher-frequency details. In Section 5, we transform a single image to a plausible bas-relief. We formulate the problem using a variational framework in Section 6. Results and comparisons are shown in Section 7. We conclude the paper with future work in Section 8.