# Quality Assessment of 3D Synthesized Images Based on Textural and Structural Distortion Estimation
## 3 The Proposed Technique
### Estimating the Textural Distortion  
Textures are complex visual patterns, composed of spatially organized entities that have characteristic brightness, color, shape, and size. The texture is an important discriminant characteristic of an image region [53] and can be used for various purposes such as segmentation, classification, and synthesis [54]. Image texture gives us information about the spatial arrangement of color or intensities in an image or a selected region of an image. During the process of DIBR, the texture of the synthesized image can be adversely affected due to object shifting, incorrect rendering of textured areas, and blurry regions [55]. Object shifting may cause translation or changes in the size of the region in the synthesized view. Due to the translation of objects, the occluded areas in the original view may become visible in the synthesized view, and these are known as holes. These holes are usually estimated using image inpainting techniques that do not always produce accurate reconstruction and result in the incorrect rendering of texture areas and blurry regions in the synthesized view. Given a DIBR-synthesized image and its corresponding reference, the proposed metric estimates the texture distortion by computing the local variations in their contrasts.  
Image contrast is an important feature of texture, a basic perceptual attribute and also an important characteristic of the human visual system (HVS) [56; 57]. Contrast sensitivity is one of the dominating factors in the research of visual perception [58]. It can be defined as the difference between luminance or color that makes the representation of an object distinguishable. The most famous contrast computation methods are the Michelson and Weber contrast formulas [58]. There are a few methods that use some form of contrast to assess the quality of images [59; 60; 61].  
The proposed metric captures the local variation in contrast of the synthesized image and its reference image. The two images are low-pass filtered to smooth their high spatial frequencies. This is achieved with a small Gaussian filter \(w\) of size \(3\times 3\).  
\[w_{ij}=\frac{1}{\alpha_{g}}\exp(\frac{i^{2}+j^{2}}{2\sigma_{g}^{2}}) \tag{1}\]  
where \(\alpha_{g}\) is a normalization term that ensures \(\sum w_{ij}=1\) and \(\sigma_{g}\) is Gaussian variance, which controls the weight distribution and the filter size. Let \(I\) and \(R\) be the filtered synthesized image and its reference image of size \(M\times N\). Let \(x_{ij}\) represent a block of size \(m\times n\) in image \(I\) centered at pixel \((i,j)\), and \(y_{ij}\) be its corresponding block in reference image \(R\) centered at pixel location \((i,j)\). Let \(x_{i}\) and \(y_{i}\) represent the i-th corresponding blocks of \(I\) and \(R\). The mean \(\mu\), variance \(\sigma^{2}\), and standard deviations \(\sigma\) of a block \(x_{ij}\) are computed.  
\[\mu_{ij}=\frac{1}{mn}\sum_{a=-\frac{m}{2}}^{\frac{m}{2}}\sum_{b=-\frac{n}{2}}^ {\frac{n}{2}}x(i+a,j+b) \tag{2}\]  
\[\sigma_{ij}^{2}=\frac{1}{mn-1}\sum_{a=-\frac{m}{2}}^{\frac{m}{2}}\sum_{b=- \frac{n}{2}}^{\frac{n}{2}}(x(i+a,j+b)-\mu_{x_{ij}})^{2} \tag{3}\]These statistics for \(y_{ij}\) are computed analogously. The variation in contrast \(\psi_{ij}\) between the blocks \(x_{ij}\) and \(y_{ij}\) is then computed.  
\[\psi_{ij}=\frac{2\sigma_{ij}\sigma_{ij}+c}{\sigma_{ij}^{2}+\sigma_{ij}^{2}+c} \tag{4}\]  
where \(c\) is a small constant used to stabilize the equation. The \(\psi\) scores of all pixels in \(I\) are computed and averaged to obtain the texture distortion score \(T\) of the synthesized image.  
\[T=\frac{1}{MN}\sum_{i=1}^{M}\sum_{i=1}^{N}\psi_{ij} \tag{5}\]