Introduction

1.1. Motivation

In the nature, a real scene has a high dynamic range of intensity, while the current monitor can only display the low dynamic range image. Human eyes can percept high dynamic range image (HDRI). Recently, HDR image can be reconstructed from a set of photographs of the scene captured under different exposure times [2][3][4]. Several researchers develop novel hardwares to capture the HDR image [5][6]. Thus we can preserve all detail in the scene without loss of information in the areas that are over- or under-exposured.

Since the technique of the display device is low dynamic display system. Therefore, we need an additional technique, called tone mapping, to compress HDR image into LDR image without losing the fine detail.

In this thesis, our method applies HDR image and tone mapping techniques to preserve the fine detail of the image. The objective is to make the contrast in the dark area and the bright area as same as possible. We extent Fattal et al. [8] work to achieve our goal. Take Figure 1.1 for an example. First, we capture an image containing shadow, and compute the gradient of the image. Then, we mask the area of the shadow edge and set the shadow gradient to zero. After reconstructing the image from the new gradient map, we find that the shadow part in the image is gone.

Based on these ideas, we want to design an algorithm to remove the shadow effect in the image.

(a) The original image (b) The gradient magnitude of the left image

(c) The new gradient magnitude with set the area of the shadow edges to zero

(d) The reconstructed from the new gradient magnitude

Figure 1.1 The gradient based shadow removal method.

1.2. Related work

Tone mapping methods can be classified into two main groups [21]: tone reproduction curves (TRCs) and tone reproduction operators (TROs). The main pros of TRCs are simplicity, computational efficiency, and preserved relative contrasts. However, the main cons of them are loss of local contrasts in images. The typical TRC approaches are gamma correction, histogram equalization, and so on.

On the contrast, TROs are easy in preserving local contrasts in images, but more complex on computation. The TRO methods can be classified into three groups: human vision system (HVS) base, filter based, and gradient base. HVS based researchers use the computational

model proposed by the work of the psychologists such as [20]. Filter based researchers want to separate original images into reflectance (also called detail or intrinsic image) and illuminance (also called base) images. The basic idea is that the image f(x,y) is regarded as a product,

( ) ( )

f x, y = I(x, y)R x, y

where R(x, y) is the reflectance and I(x, y) is the illuminance at each point (x, y). If the reflectance and illuminance image can be separated perfectly from the original image, then the HDR image can be compressed by scaling down the illuminance image to get a new illuminance image and re-multiplying the reflectance image. While taking logarithm on the both sides in equation

(

Filter based researchers assume that the local variance of the illuminance image is smaller than the local variance of the reflectance image. This means that the illuminance image is smoother than the reflectance image. In other words, the illuminance image has a lower spatial frequency. Therefore, filter based researchers develop the smoothing filter to estimate illuminance image, such as unilateral [16], bilateral [17], trilateral [18], homomorphic filter [19], PDE based algorithm (e.g. anisotropic diffusion equation [13], shock filter [14], low curvature image simplifier (LCIS) [15], and so on) or other noise reduction algorithm (e.g.

Wiener filter [26]). But these approaches might cause halo artifacts. Gradient based approaches [8], which we would use in this thesis, compute the new gradient magnitude map from the original one at first, and then reconstruct image from this new map (see section 2.2 and 3.3 for more detail).

The shadow removal algorithm proposed by [10] uses the classifier to classify whether the edge is the shadow edge or not. Although this algorithm is well performed, it needs a lot of training patterns, and it is computationally inefficient. This is not useful to the surveillance or

some probability model estimated from the image sequence in order to determine whether there is shadow or not. Another group of researchers [22][23][24][25] use the chromatic property.

They could succeed to eliminate shadow, but there are two problems that would occur. The first problem is that for the gray level colors the rule they suggest would fail. In other words, for the white paper with black words, they determine the black words as “shadow” (see Figure 1.2 for an example). Another problem is that for the lossy compression image [26] (e.g. JPEG image) the chromatic property would be destroyed acutely (see Figure 1.3 for an example). This might cause the decision rule fail. This is because the lossy compression technique assumes that the human eyes are more sensitive to the luminance channel than the chromatic channel. Therefore, it compresses the chromatic channel more heavily than the luminance channel. In other words, we would destroy more information on the chromatic channel. Thus if we want to remove shadow in the lossy compression image, we need to overcome this problem first.

(a) The original image (b) Results obtained by Finlayson et al.[24] method Figure 1.2 Results obtained by Finlayson et al.[24] method. The gray texture on the football is lost.

(a) The original image (b) The Hw property of (a) without compression

(c) The Hw property of (a) with compression

Figure 1.3 Compare the Hw property [28]. The compression technique would affect the result.

1.3. Contribution

The contributions of this thesis can be summarized as follows:

1. We extent the Fattal et al. [8] work to reduce the shadows in the static image.

2. We succeed in reducing the shadows by removing fuzzy edge.

1.4. Outline

Our proposed method is divided into four steps. The flow chart is given in Figure 1.4. The remainder of this thesis is organized as follows: Chapter 2 describes how to adjust camera curve and how to reconstruct the image from the gradient field. Chapter 3 gives the fundamental concept on the edges, and shows how to design a desired gradient attenuation function step by step. Chapter 4 gives some experimental results o our implementation of the proposed method.

Finally, some conclusions and future work are presented in Chapter 5.

Figure 1.4 The flow chart of our system