A No-Reference Perceptual Blur Metric

3rd European Workshop on Visual Information Processing, 2011

This paper presents an efficient no-reference metric that quantifies perceived image quality induced by blur. Instead of explicitly simulating the human visual perception of blur, it calculates the local edge blur in a cost-effective way, and applies an adaptive neural network to empirically learn the highly nonlinear relationship between the local values and the overall image quality. Evaluation of the proposed metric using the LIVE blur database shows its high prediction accuracy at a largely reduced computational cost. To further validate the performance of the blur metric on its robustness against different image content, two additional quality perception experiments were conducted: one with highly textured natural images and one with images with an intentionally blurred background 1 . Experimental results demonstrate that the proposed blur metric is promising for real-world applications both in terms of computational efficiency and practical reliability.

This paper presents a no-reference image blur metric that is based on the study of human blur perception for varying contrast values. The metric utilizes a probabilistic model to estimate the probability of detecting blur at each edge in the image, and then the information is pooled by computing the cumulative probability of blur detection (CPBD). The performance of the metric is demonstated by comparing it with existing no-reference sharpness/blurriness metrics for various publicly available image databases.

Blur estimation in image processing has come to be of great importance in assessing the quality of images. This work presents a survey of no-reference blur estimation methods. A no-reference method is particularly useful, when the input image used for blur estimation does not have an available corresponding reference image. This paper provides a comparison of the methodologies of four no-reference blur estimation methods. The first method applies a scale adaptive technique of blur estimation to get better accuracy in the results. The second blur metric involves finding the energy using second order derivatives of an image using derivative pair of quadrature filters. The third blur metric is based on the kurtosis measurement in the discrete dyadic wavelet transform (DDWT) of the images. The fourth method of blur estimation is obtained by finding the ratio of sum of the edge widths of all the detected edges to the total number of edges. The results provided are useful in comparing the methods based on metrics like Spearman correlation coefficient. The results are obtained by evaluation on images from the Laboratory for Image and Video Engineering (LIVE) database. The various methods are evaluated on the images by adding varying content of noise. The performance is evaluated for 3 different categories namely Gaussian blur, motion blur and also JPEG2000 compressed images. Blur estimation finds its application in quality assessment, image fusion and auto-focusing in images. The sharpness of an image can also be found from the blur metric as sharpness is inversely proportional to blur. Sharpness metrics can also be combined with other metrics to measure overall quality of the image.

IEEE International Conference on Imaging Systems and Techniques (IST’2013), Beijing, China, 2013

Blur metrics have been used in broad range of applications to quantify the amount of blur especially in images. The spatially varying blur due to defocus or camera shake is hard to estimate. It is observed that the existing blur metrics does not perform well for images having very few or many features. In this work, we present contrast based blur invariant features named as CBIF, which utilizes useful information available in different contrast levels. We further, used CBIF along with local standard deviation to formulate a no reference objective blur metric which shows better results compared with other existing blur metrics. Additionally, the proposed blur metric can be modified for perceptual quality assessment by implementing the scheme which takes advantage of a better correlation with human blur perception. Also, the blur metric can be modified to provide blur assessment in the presence of gaussian noise. The proposed metric is monotonic as well as accurate even for severely blurred images. The comparison of results with subjective scores of CSIQ and LIVE image databases also validated the superiority of our proposed metric over existing metrics. The applicability of our blur metric is also demonstrated for the assessment of JPEG distortions. The property of CBIF for being more sensitive to blur effected regions is also used for obtaining blur likelihood map which is further used in blur segmentation.

Signal Processing: Image Communication, 2018

Blurring is a common artefact detrimental to the image quality. It affects especially edges and texture features that represent high frequency components of an image. The purpose of this paper is to propose a simple, fast, and faithful measure able to blindly assess blur amount in images. The main idea turns on analysing the frequency response at the muliresolution transitions. To achieve that, the histogram of the DCT coefficients of the edge map is modelled by using an exponential probability density function (pdf). Tests revealed that the steepness of the pdf depends on the blur amount, hence, it is used as a cue to characterize the blur effect. Comprehensive testing demonstrates good consistency of the proposed measure with subjective quality scores as well as satisfactory performance when compared with representative state-of-the-art blind blur quality measures.

Image Quality and System Performance VIII, 2011

The perceptual quality of digital imagery is of great interest in many applications. Blur artifacts can be among the most annoying in processed images and video sequences. In many applications of perceptual quality assessment, a reference is not available. Therefore no-reference blurriness measures are of interest. In this paper, we present a universal, referencefree blurriness measurement approach. While some other methods are designed for a particular source of blurriness such as block-based compression, the proposed is universal in that it should work for any source of blur. The proposed approach models the gradient image of the given image as Markov chain and utilizes transition probabilities to compute a blurriness measure. This is the first time that transition probabilities are applied to perceptual quality assessment. Specifically, we first compute the transition probabilities for selected pairs of gradient values and then combine these probabilities, using a pooling strategy, to formulate the blurriness measure. Experimental studies compare the proposed method to the state-of-the-art reference-free blurriness measurement algorithms and show that the proposed method outperforms the commonly used measures.

Lecture Notes in Computer Science, 2009

A new free reference image quality index based on the perceptual blur estimation is proposed. Here, we limit the study to isotropic blurring degradation although the principle could be extended to other distortions. The main idea developed here is to exploit the limitation of the blurring discriminability of the Human Visual System (HVS). The proposed method consists of adding a small amount of blur to the image and measuring its impact on the image quality level. From the two images, a perceptual map is then obtained using some HVS characteristics. A quality index is finally derived by extracting some geometrical features from the blurring map visibility. The obtained results are compared with some known methods.

1996

Transformadas de Laplace

Revista de Arqueologia

Este texto propõe debater sobre os processos de seleção e sobre as políticas de preservação de Bens Culturais em Pelotas-RS. Uma análise sobre o reconhecimento do conjunto histórico, que buscou entender as articulações municipais e federais na proposta de preservação, evidenciou uma predileção à valorização da arquitetura eclética dos séculos XIX e XX como Bens Culturais representativos da história local. A partir de uma aproximação entre a perspectiva crítica dos estudos sobre patrimônio e a Arqueologia da Arquitetura, procuramos identificar tratativas contradiscursivas sobre o patrimônio edificado local, evidenciando o papel social do fazer arqueológico no reconhecimento de patrimônios invisibilizados. Como exemplos serão abordados o Passo do Negros e a zona industrial do Porto de Pelotas.

This book is a revision of the sixth edition, published in 1996. That edition has served, just as the earlier ones did, as a textbook for a one-term introductory course in the theory and application of functions of a complex variable. This edition preserves the basic content and style of the earlier editions, the first two of which were written by the late Ruel V. Churchill alone. In this edition, the main changes appear in the first nine chapters, which make up the core of a one-term course. The remaining three chapters are devoted to physical applications, from which a selection can be made, and are intended mainly for selfstudy or reference. Among major improvements, there are thirty new figures; and many of the old ones have been redrawn. Certain sections have been divided up in order to emphasize specific topics, and a number of new sections have been devoted exclusively to examples. Sections that can be skipped or postponed without disruption are more clearly identified in order to make more time for material that is absolutely essential in a first course, or for selected applications later on. Throughout the book, exercise sets occur more often than in earlier editions. As a result, the number of exercises in any given set is generally smaller, thus making it more convenient for an instructor in assigning homework. * These polynomials are called Chebyshev polynomials and are prominent in approximation theory. SEC. 8 FIGURE 10 ROOTS OF COMPLEX NUMBERS 23 true when 0 is decreased by 2,7. It is, therefore, evident from Fig. 10 that two nonzero complex numbers z1 = rlei61 and z2 = r2eie2 are equal if and only if r1= r2 and 01 = 02 + 2k7r, where k is some integer (k = 0, +1, ±2, ...). This observation, together with the expression zn = rneine in Sec. 7 for integral powers of complex numbers z = rei0, is useful in finding the nth roots of any nonzero complex number zo = rpei°0, where n has one of the values n = 2, 3, .... The method starts with the fact that an nth root of za is a nonzero number z = rei0 such that zn = z0, or rneinO = rceie0. According to the statement in italics just above, then, and nO=00+2kir, (e)O<argz<n/4(z34 O); Ans. (b), (c) are domains. (d) Im z = 1; (f)Iz-4!>>lzl. 2. Which sets in Exercise I are neither open nor closed? Ans. (e). 3. Which sets in Exercise 1 are bounded? Ans. (a). 4. In each case, sketch the closure of the set: (a)-rr < arg z < 7r (z 34 0); (b)JRezj<Izi; (c) Re C L < 1; (d) Re(z2) > 0. z 2 32 COMPLEX NUMBERS CHAP. I 5. Let S be the open set consisting of all points z such that I z I < 1 or (z-21 < 1. State why S is not connected. 6. Show that a set S is open if and only if each point in S is an interior point. 7. Determine the accumulation points of each of the following sets: (a) z = i" (n = 1, 2, ...); (b) z,, = i"/n (n = 1, 2, ...); (c) 0 < arg z < n/2 (z 34 0); (d) zn = (-1)n(1 + i) n n 1 (n = 1, 2, ...). Ans. (a) None; (b) 0; (d) ±(1 + i). 8. Prove that if a set contains each of its accumulation points, then it must be a closed set. 9. Show that any point zp of a domain is an accumulation point of that domain, 10. Prove that a finite set of points z1, z2, ... , z, cannot have any accumulation points. CHAPTER 2 ANALYTIC FUNCTIONS We now consider functions of a complex variable and develop a theory of differentiation for them. The main goal of the chapter is to introduce analytic functions, which play a central role in complex analysis.