Idea: The aim of this study is to develop methods which simulate how the human eye analyses a scene. In particular distortion measures, based on visibility laws, are defined and used in the detection of complicated objects over different backgrounds . The use of visibility-based methods allows for a fully automatic process. The distortion based methods are aimed at the detection of semi-transparent blotches on archived photographs.
Observations:
1. blotches are visible at the first glance, independently of the content of the image;
2. they are slightly colored regions but not uniform, even though they are perceived as uniform;
3. they are not characterized by a regular shape and they can have different sizes from few pixels to large regions, even in the same image;
4. they can be dark or slight and they are almost semitransparent they do not completely cover the original content of the image. Therefore, they can be also perceived in highly detailed regions of the image, as shown in the example above.
Therefore, it is hard to find a precise feature for these defects since they can be easily confused with scene components.
Nonetheless,
Blotches are perceived as homogenous areas of the image, independently of the image features, due to the low-pass behaviour of the Human Visual System (HVS). To simulate this, a low-pass filter is applied to the saturation image.
The order of the filter is chosen as that which gives the minimum perceivable contrast (0.02) between two successive blurred images. The contrast, given by Peli (1990) is defined as:
Blotches always are visible bright objects in the Saturation component.
Therefore, they can be detected through a thresholding operation. The threshold value has to correspond to the point of maximum visibility of two different components of the image: degradation and clean information.
Two new distortion measures can be introduced. The first one, D1,
D1 measures the change of perception of two different objects (I and IT(t)) on a fixed background M. In otherwords it evaluates how the visibility of an object of intensity I(x; y) changes if it is substituted for the threshold value T(t).
As it is shown in the image above, it grows quickly in its first part since the thresholding involves less uniform regions with small area. In the second part, the behaviour changes since many points having values close to the background are selected.
The second distortion D2 measures the change of the contrast of the same object I over different backgrounds (MT(t) and M):
D2 is the product of two different components: the first one is I/MT(t), which is a growing function with respect to the time t, i.e. as MT(t) decreases, while the second one, (MT(t)-M)/M, is a decreasing function converging to zero.
As the figure above shows, in the first part of the function the term (MT(t)-M)/M gives a minor contribution since the thresholding operator involves few pixels and then MT(t) does not change significantly. On the contrary, in the second part MT(t) approaches M faster, as a lot of points close to the background are selected, then D2 approaches zero.
It is possible to combine the opposite behaviour of the two distortion measures as follows
from which it is possible to gather the following rate-distortion curve:
Some references
V. Bruni, A. Crawford, A. Kokaram, D. Vitulano, "Visual perception of semi-transparent blotches: detection and restoration", chapter in I-Tech Book: Brain, Vision and AI, 2008
V. Bruni, A. Crawford, A. Kokaram, D. Vitulano, "Multi-scale semi-transparent blotch removal on archived photographs using Bayesian matting techniques and visibility laws", Proc. of IEEE Int.Conf. on Image Processing 2007, vol. 1, pp. 561-564, S. Antonio,Texas, September 2007
V. Bruni, A. Crawford, A. Kokaram, D. Vitulano, "Digital removal of blotches with variable semi-transparency using visibility laws",Proc. of Int. Conf. on Brain Vision and Articial Intelligence BVAI 2007, special issue on Lecture Notes in Computer Science, pp. 254-263, Napoli, October 2007
V. Bruni, E. Rossi, D. Vitulano, A Model for the Restoration of Semi-transparent Defects Based on Lie Groups and Human Visual System, Computer Vision, Imaging and Computer Graphics. Theory and Application, Communications in Computer and Information Science serie, Springer, vol. 0359, pp. 354-368, 2013, selected paper in VISAPP 2012.
V. Bruni, A. Crawford, A. Kokaram, D. Vitulano, "Semi-transparent Blotches Removal from Sepia Images Exploiting Visibility Laws", Signal Image and Video Processing, Springer, vol. 7, no. 1, pp. 11-26, Jan. 2013.
V. Bruni, E. Rossi, D. Vitulano, Automated Restoration of Semi-Transparent Degradation via Lie Groups and Visibility Laws, Mathematics and Computers in Simulation, Elsevier Science, vol. 106, issue C, pp. 109-123, 2014.