A Comparative Analysis of Motion-Blur Magnitude Parameter Estimation Techniques

DOI : 10.17577/IJERTV3IS20746

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A Comparative Analysis of Motion-Blur Magnitude Parameter Estimation Techniques

Rupali M. Bora,


Smita N. Chaudhari,


Prajakta S. Vispute


Abstract-Motion blur in a digital image is caused due to motion of an object while capturing it. This motion blur may cause sig- nificant problems for image processing algorithms. So, it may be required to remove it from the image or identify inconsistency of it in an image for tempering detection.

The magnitude and direction are two parameters of mo- tion blur used to distinguish it from rest of the image. Here, three algorithms are discussed for estimation of this magnitude parameter. They are viz. a. Radon transform based b. Cepstral Method c.PBM (Perceptual Blur Metric) Based. The results are compared for accuracy and execution time required. PBM based method gives optimum results considering both parameters.


    Motion blur is caused by the relative motion between the camera and the pictured object during the time the shutter is open. As blurring can significantly degrade the visual quality of images, many researchers have been working either on preventing motion blurring during image capturing or on post-processing of the image to remove motion blur.

    The slow speed of the camera shutter relative to the

    For uniform motion blur, the process of blurring is usually modelled as the following convolution:

    I=(H*P)+ N (1)

    where I is the blurred image, H is the sharp image, P is the blurring kernel, and N is the noise present.

    For a horizontal uniform velocity motion blur, the blur- ring kernel P can be modelled as P = 1/L[1 1.1]1xL, where L is the length of the kernel. Note that a directional blurring kernel P can be formulated by rotating P by degrees about the x-axis.

    To identify the amount of blurring from its blurred version I, parametric knowledge of the blurring kernel P is required. Methods for calculating the magnitude parameter of motion blur are discussed next [1][4].

      1. Radon Transform method based on image gradient

        A periodic pattern that is easier to detect also exists in the gradient of blurred image in the spectral domain. Differentiat-

        object being imaged is one of the possible causes of motion blur. Camera shake is found to be the culprit for the presence

        ing (1),

        I HP N


        of motion blur in many images. Reducing the exposure inter-

        Taking the Fourier transform and omitting the noise term

        val of the camera is a possible solution, but this often affects the parameters like amount of noise or depth of field ad-

        I() H ()P()


        versely. Some hardware like tripods and flashes also offer solutions to the problem of motion blur by allowing for more stable exposures or greater illumination in a short interval of time, respectively, but these are often impractical. Hence, many images containing motion blur do exist and so, it is useful to utilize the inconsistencies in motion blur in order to detect image tampering.


    Motion blur can be modelled by averaging the instantaneous

    intensity falling on a pixel over the shutter interval. Such an averaging process can be weighted by a soft Gaussian win-

    The Radon transform, which is widely used for detect-

    ing straight lines in noisy images, is used[5][6]. For a motion- blurred image, there are periodic large negative lines in

    log | I | with slope and periodicity proportional to L value. Denoting the Radon transform by R, R( log | I | ), will have periodic peaks located at (±1/L,90-), (±2/L,90-), (±3/L,90-)..Therefore, this should correspond to a peak in the Fourier transform of R( log | I |). Calculating Fourier transform of this Radon transform, the peak occurs at

    ( ,)

    dow instead of using the idealized shutter interval, in order to allow for non-ideal mechanical shutter effects. Alternatively,


    1 and


    90 0


    blurs arising from motion, like other types of blur, can also be considered as convolving an in-focus image with a blur kernel in the spatial domain. The motion blur kernel is determined by the relative velocities of the camera and the objects in the image.

    Blur Model:

    This estimated motion blur is represented as a two-element

    vector = [mag, dir], where mag = L and dir = . Here L and are motion blur parameter [1].

      1. Cepstral Method

    As the degraded image is the result of convolution with the blur model, it is impossible to separate the blur in spatial do- main. However, the blur information can be easily extracted in cepstrum domain. The cepstrum of an image I is defined as [3],

    C =F1 {log(| |)} (5)

    where is the Fourier transform of motion blurred image I,

      1. Radon Transform Method

        The graph of fig. 3 shows the linearity of blur parameter magnitude values for a range of nearly 10 to 50 are accurate.

      2. PBM variation Method

    The graph of fig.4 shows the linearity of blur parameter mag- nitude values for a wide range of 1-50 and nearly accurate.


    and F1 is the inverse Fourier transform. As Eq. (5) shows, the image in cepstrum-domain is the inverse Fourier trans- form of the logarithm power spectrum of the original image.

    2.3 PBM variation method

    The L value is calculated using Perceptual Blur Metric [2]. Let S be the set of edge pixels in the binary edge map of im- age obtained by applying the Sobel operator in the vertical, horizontal and diagonal directions. A modified metric, named as oriented blur metric PBM, is defined as [1]


    Output 40

    magnitu 30

    de 20



    1 9 17 25 33 41 49

    Input magnitude (L)

    Actual Blur Magnitu de

    Cepstral Method Magnitu de

    E( p)


    PBM (I ) pS


    Fig. 2 Actual Vs. Cepstral method magnitude


    where E(p) is the width of the edge along the direction per- pendicular to at the edge pixel p and |.| denotes cardinality. The oriented PBMs are computed for orientations i, i=1 to t, where t is the number of orientations evaluated and then de-


    Output 200

    Magnit 150



    fine the overall PBM as,

    PBM(I)=max(PBMi)i (7)

  3. Results and Comparison

    1. Test data for parameters estimation

      The images with the range 1-50 of motion blur magnitude and a fixed theta are generated and checked against all three





      1 8 15 22 29 36 43 50

      Input Magnitude (L)



      methods for magnitude estimation. The fig.1 shows different images for testing.

      Fig. 3 Actual Vs. Radon Transform method magnitude


      50 Actual

      Output magnit ude






      1 9 17 25 33 41 49

      Input Magnitude (L)

      Blur Magnit ude

      Calculat ed PBM

      Fig. 1 test images a. Cameraman b. Lena c. Car d. Jerusalem

    2. Cepstral Method

      The graph of fig. 2 shows the linearity of blur parameter magnitude values in the range of middle values from 5-25 only.

      Fig. 4 Actual Vs. PBM variation method magnitude

        1. Performance bounds

          The time required for PBM based method used for estimation of motion blur magnitude parameters is minimum among all. The accurac for PBM based method is good for a wide range of input values (1-50).

          As shown in fig. 5, time computation is done for a set of images of magnitude values in range of 1-50 and direction

          angle 45. It shows Radon transform method requires maxi- mum time for magnitude estimation. Cepstral method requires minimum time but accuracy is less in this method as shown in fig. 2. Hence PBM variation is best to use for further process- ing.

          Time require d (milisec onds)

          Execution Time







          Fig. 5 Execution Time of Cepstral, Radon transform and PBM variation methods for magnitude estimation


As motion blur in an image can be characterised by two pa- rameters viz. Magnitude and direction. For magnitude pa- rameter estimation, a comparative analysis of the three tech- niques, viz. PBM based, Cepstral based, Radon Transform based, is done.

The techniques are compared for 4 test images with variation of magnitude values from 1-50. The experimental results show that the PBM based method gives fast results for an image with a good accuracy over a wide range of magni- tude parameter values.


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      2. P. Marziliano, F. Dufaux, S.Winkler, and T. Ebrahimi, A no- reference perceptual blur metric, in Proc. IEEE Int. Conf. Image Processing, Citeseer, 2002, vol. 3, pp. 5760.

      3. Shiqian Wu, Zhongkang Lu, Ee Ping Ong, Weisi Lin, Blind image blur identification in Cepstrum Domain, IEEE 2007, pp.1166-1171

      4. Bora, R.M., Shahane, N.M. , Image forgery detection through motion blur estimates, in Proc. Computational Intelligence & Computing Research (ICCIC), 2012 IEEE Int. Conf., pp. 1-4

      5. H. Ji and C. Liu, Motion blur identification from image gra- dients, in Proc. IEEE Conf. Computer Vision and Pattern Recognition, 2008, pp. 18.

      6. Hongwei SUN, Michel Desvignes, Yunhui YAN, Weiwei LIU, Motion Blur Parameters Identification from Radon Transform Image Gradients, IEEE 2009, pp. 2098 – 2103.

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