Evaluation of Vision based Surface Roughness using Wavelet Transforms with Neural Network Approach

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					                                                              (IJCSIS) International Journal of Computer Science and Information Security,
                                                                                                              Vol.8, No. 8, November 2010



 Evaluation of Vision based Surface Roughness using
 Wavelet Transforms with Neural Network Approach
                 *T.K.Thivakaran                                                        **Dr.RM.Chandrasekaran
                 *Research Scholar,                                                     **Professor, Department of CSE,
                  MS University,                                                          Annamalai University,
                  Tirunelveli – 627012.INDIA                                              Chidambaram – 620 024.INDIA


Abstract---Machine vision for industry has generated a great             result in inconsistent estimation of roughness of
deal of interest in the technical community over the past                components using machine vision primarily due to the fact
several years. Extensive research has been performed on                  that illumination, shadow on the images is likely to be
machine vision applications in manufacturing, because it has             different.
the advantage of being non-contact and as well faster than the
contact methods. Using Machine Vision, it is possible to
                                                                                   In this work, the machined surfaces are captured
evaluate and analyze the area of the surface, in which machine           using a Machine Vision system. Following the image
vision extracted the information with the help of array of               enhancement, the features are extracted and then the
sensors to enable the user to make intelligent decision based on         roughness parameters are estimated and analyzed. Here
the applications. In this work, Estimation of surface roughness          wavelet is used to extract the features of the enhanced
has been done and analyzed using digital images of machined              image, and an artificial neural network (ANN) is developed
surface obtained by Machine vision system. Features are                  to predict the surface roughness. The results are compared
extracted from the enhanced images in spatial frequency                  with that obtained using the standard stylus method.
domain using a two dimensional Fourier Transform and
Wavelet Transform. An artificial neural network (ANN) is
trained using feature extracted values as input obtained from                            II. ROUGHNESS PARAMETERS
wavelet Transform and tested to get Rt          as output. The
estimated roughness parameter (Rt) results based on ANN is
compared with the Rt values obtained from Stylus method                  The machined surfaces are generally characterized by three
and the best correlation between both the values are                     kinds of errors (i) form errors, (ii) waviness, and (iii)
determined.                                                              surface roughness. The concept of roughness is often
                                                                         described with terms such as ‘uneven’,’ irregular’, ‘coarse
Keywords--- Surface roughness, Machine vision, Milling,                  in texture’, broken by prominences’, and other similar ones
Grinding, Wavelet Transform, Neural Network.                             (Thomas,1999). Similar to some surface properties such as
                                                                         hardness, the value of surface roughness depends on the
                      I. INTRODUCTION
                                                                         scale of measurement. In addition, the concept roughness
                                                                         has statistical implications as it considers factors such as
The quality of components produced is of main concern to                 sample size and sampling interval. The one parameter that
the manufacturing industry, which normally refers to                     is standardized all over the world and is specified and
dimensional accuracy, form and surface finish. Therefore,                measured far more frequently than any other is the
the inspection of surface roughness of the work piece is                 arithmetic average roughness height, or Roughness
very important to assess the quality of a component, which               Average. Universally called Ra, it was formerly known as
is normally performed using stylus type devices, which                   AA (Arithmetic Average) in the United States and CLA
correlate the vertical displacement of a diamond-tipped                  (Center Line Average) in the United Kingdom. It is defined
stylus to the roughness of the surface under investigation.              as the arithmetic mean of the departures of the profile from
But, the limitations of stylus techniques have already been              the mean line.
reported in detail in [6, 5, 4]. Machine Vision typically
employs a camera, a frame grabber, a digitizer and a                     Rq (or also known as RMS) is the root mean-square
processor for inspection tasks where precision, repetition               average of the departures of the roughness profile from the
and/or high speed are needed. The histograms of the surface              mean line. Rq has statistical significance because it
image have been utilized to characterize surface roughness               represents the standard deviation of the profile heights and
and quality. Fourier transform (FT) of the digitized surface             it is used in the more complex computation of skewness,
image in which the magnitude and frequency information                   the measure of the symmetry of a profile about the mean
obtained from the FT are used as measurement parameters                  line.
of the surface finish. These methods use the basic
assumption that the surface of the specimen is completely
flat and there is no inclination when the images are
captured. Even a small inclination of the specimen may                                         … (1)

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                                                                       Fig. 1(a), (c) The profiles obtained for a turned component
 A. Profiles for Turned Machined Components                            with a stylus instrument. (b), (d) the gap profiles obtained
                                                                       for the same turned components by diffraction method.
    Figure 1(a) and figure 1(c) shows the profiles obtained
for a turned component with a stylus instrument. Similarly,               B. Profile for Ground Machined Components
figure 1(b) and 1(d) shows the gap profiles obtained for the              Figure 2(a) shows the profiles obtained for a ground
same turned components by diffraction method. In both                  component with a stylus instrument. Similarly, figure 3(b)
graphs, ‘z’ is the deviation of the points on the profile from         shows the gap profiles obtained for the same ground
the mean-line. It can be observed that appreciable                     components by diffraction method. In both graphs, ‘z’ is the
differences in the diffraction pattern are seen for large              deviation of the points on the profile from the mean-line.
variations in the gap and therefore good comparison of
results is guaranteed in both only for turned components of
medium roughness. For very rough surfaces scattering is
observed. A limitation in the usage of the different methods
is that the smoothness of the edge plays a crucial role in the
evaluation of the finish of the components.




                                                                       Fig. 2(a) The profile obtained from a ground component
                                                                       with a stylus instrument, (b) The gap profile obtained for
                                                                       the same ground component by diffraction method.

                                                                         III. SPECTRUM TECHNIQUES FOR FEATURE EXTRACTION

                                                                          A. Fourier spectrum
                                                                          The Fourier spectrum is the frequency domain
                                                                       counterpart of the autocorrelation function. The FT of the
                                                                       correlation is used, which corresponds to the power spectral
                                                                       density function and describe how the power in a signal is
                                                                       distributed over frequency. The power spectrum can reveal
                                                                       the presence of offset, or periodic structures in a data set.

                                                                          B. Wavelet Transform (WT)
                                                                          The wavelet is a tool in surface texture analysis and can
                                                                       decompose a surface into multi-scale representation in a
                                                                       very efficient way. The wavelet transform (WT) is a
                                                                       mapping of the signal to the time-scale joint representation.
                                                                       By WT, the decomposition of a signal with a real


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orthonormal bases Ψmn(x) obtained through translation and                     where,ψ H ( x, y ) , ψ V ( x, y ) and ψ D ( x, y ) are called the
dilation of a kernel function Ψ(x) known as mother wavelet                    horizontal, vertical and diagonal wavelets. Thus, DWT is
as given in eqn. [2],                                                         well localized and allows decomposition in three directions,
                                                                              namely, horizontal, vertical and diagonal respectively.
                                                 … (2)                           D. Features of Wavelets
Where, m,n are integers. To construct the mother wavelet                         In this application, the features are extracted using a
Ψ(x), it is required to determine a scaling function φ(x)                     wavelet which belongs to a family of orthogonal wavelets.
given in eqn. [3],                                                            The mother wavelet (DB4), its corresponding scaling and
                                                                              wavelet functions and the decomposition filters are shown
                                                                              in Figure 3 and Figure 4 respectively.
                                               … (3)
Then, the mother wavelet Ψ(x) is related to the scaling
function as in eqn. [4],

                                                          … (4)
where,

The coefficients h(k) have to meet several conditions for the
set of basis wavelet functions to be unique, be orthonormal                                            Fig. 3 wavelet extraction
and also have a certain degree of regularity.

   C. Wavelet Transform for Signals
   In two dimensional cases, the one dimensional wavelet
transforms are applied along both the horizontal and
vertical directions φ ( x) is a one dimensional real, sequence
integral    scaling      function    defined   as     in   [5]
                j
φ j , k ( x ) = 2 2 φ (2 j x − k )                        … (5)                 Fig. 4 Decomposition of low-pass filter h φ(-n) and high-
        Translation k determines the position of this one                                         pass filter h ψ(-m)
dimensional function along the x- axis, scale j determine its
                                             j                                The DB4 scaling function is given by
width along x axis and 2 2 controls its height and                            ai = h0 s2i + h1s2i +1 + h2 s2i + 2 + h3 s2i +3                         …(10)
amplitude. This one dimensional scaling function satisfies
these conditions:                                                             a [i ] = h0 s [ 2i ] + h1s [ 2i + 1] + h2 s [ 2i + 2] + h3s [ 2i + 3]   … (11)
         φ j ,k is orthogonal to its integer translates.
                                                                              The Daubechies DB4 wavelet function is given by
          The set of functions that can be represented as a
          series expansion of φ j ,k at low scale is contained
                                                                              ci = g0 s2i + g1s2i +1 + g 2 s2i + 2 + g3 s2i +3 … (12)
                                                                              c [i] = g0 s [ 2i] + g1s [ 2i +1] + g2 s [ 2i + 2] + g3s [ 2i + 3]      … (13)
          within those at higher scale.
So, the difference between any two sets of                φ j ,k   is              IV. NEURAL NETWORKS FOR SURFACE ROUGHNESS
represented by a companion wavelet function ψ j , k defined
                                                                                                                ASSESSMENT
                                                                              The roughness features extracted from the machined
                                j                                             images, are fed as input to an ANN to predict the roughness
in eqn. [6], ψ j , k ( x) = 2       2
                                        ψ (2 j x − k )                        value Rt. ANN consists of a number of elementary units
… (6)                                                                         called neurons. A neuron is a simple processor, which can
         Then, the 2 dimensional DWT functions are the                        take multiple inputs and produce an output. Each input into
linear products of scaling and wavelet functions φ ( x)                       the neuron has an associated weight that determines the
                                                                              ‘‘intensity’’ of the input. The processes that a neuron
and    ψ ( x)   yielding the eqn. [7] through eqn. [9].                       performs are: multiplication of each of the inputs by its
ψ ( x, y ) = ψ ( x).φ ( y )
   H
                                                         … (7)                respective weight, adding up the resulting numbers for all
                                                                              the inputs and determination of the output according to the
ψ V ( x, y ) = φ ( x).ψ ( y )                            … (8)                result of this summation and an activation function. Data is
ψ D ( x, y) = ψ ( x).ψ ( y )                             … (9)                fed into the network through an input layer, it is processed
                                                                              through one or more intermediate hidden layers and finally


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fed out of the network through an output layer as shown in                           Horizontal,      Vertical     and    Diagonal
Figure 5.                                                                            components). Calculate the weighted standard
                                                                                     deviations of three detailed images.




                                                                                                                                    …(14)


                                                                     where,     = Standard deviation of the M detail image at ith
                   Fig. 5 Typical ANN network
                                                                                   Level
                                                                             M=H(Horizontal)/V(Vertical)/D(Diagonal)
    V. PROPOSED SYSTEM FOR SURFACE ROUGHNESS
                                                                     component
                         EVALUATION
                                                                     The standard deviation of each sub image at level i is
                                                                     weighted by the factor (1/2i-1),
The methodology and block diagram of proposed Machine
vision system is shown in Figure 6(a) and Figure 6(b).
                                                                          (iv)       Repeat steps 1-4 four times for original image
                                                                                     and images at orientation 90º, 180º, and 270 º
                                                                                     (achieved by rotating original image).

                                                                                 The final feature set consists of 4*(3L) features.


           Fig.6 (a) Block diagram of proposed system                   B. Wavelet based Feature Extraction

                                                                         Since, the wavelet coefficient are orthogonal, the
                                                                     original profile can be re-obtained after wavelet
                                                                     decomposition by simply adding the sub-scales signals as
                                                                     shown in Figure 7. Furthermore, using this simple
                                                                     summation technique the concepts of roughness, waviness
                                                                     and form can be preserved. This is reflected in Figure 8
                                                                     where, an arbitrary decomposition of a surface texture is
                                                                     obtained by casting into three frequency components,
                                                                     representing the form, waviness and roughness, using
                                                                     Daubechies wavelet of order 20. A dimensional step can
                                                                     now be cleared. Indeed, the same kind of decomposition
                                                                     process can be performed using images instead of profiles,
                                                                     because surface roughness can be measured precisely using
                                                                     for instance optical surface measurement systems. The
                                                                     arbitrary decomposition into form waviness and roughness
                                                                     of surface textures obtained by casting, grinding and
                                                                     vertical milling respectively, using wavelet of order 20 is
                                                                     shown. The roughness average of each component (i.e.
  Fig.6 (b) Methodology in the proposed computer vision              form, waviness and roughness) is also shows in order to
          system for measuring surface roughness                     illustrate the roughness scale. The measured area is of a few
                                                                     millimeters square. Hence, the wavelet tool allows the
   A. Algorithm for feature extraction                               decomposition of surfaces into form, waviness and
                                                                     roughness components and can successfully replace
    (i)         Carry out image enhancement of machined              standard filters that are commonly used in surface texture
                image                                                characterization and hence, give a solid theoretical base for
    (ii)        Subject the enhanced image to a L-level              the standardization of these filters.
                discrete wavelet decomposition.
    (iii)       At each level (i=1, 2, … L), there are four
                sub-images. One approximation image and
                three components/images (LH, HL and HH or

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Fig. 7 Multiscale decomposition of a surface texture profile         Fig. 9 Comparison of multiscale decomposition of a surface
obtained by casting under seven different scales using the           texture profile obtained by casting under seven different
wavelet of order 20                                                  scales using the wavelet of order 20 and its frequency
                                                                     normalized equivalent.


                                                                       C. ANN based surface roughness estimation

                                                                         ANN with a variation of the classic back-propagation
                                                                     algorithm is employed to predict surface roughness.
                                                                     Compared with more conventional approaches, ANN
                                                                     demonstrates certain advantages that make them much
                                                                     more attractive. They have the ability to recognize patterns
                                                                     that are similar, but not identical, it can store information
                                                                     and generalize it. There is no need for explicit statement of
Fig. 8 Multiscale decomposition of a surface texture profile         the problem or for a problem-solving algorithm. Due to
obtained by casting under three different components (form           their massive parallelism, ANNs display increased
waviness and roughness) using the wavelet of order 20.               computational power that can be used to deal with complex
                                                                     problems. Back-propagation neural network used for
In Figure 9, the FNWT maxima indicate at each scale the              estimating the surface roughness of the machined surfaces
location of a frequency component. Those features can also           with is a four layer network with six nodes in the input
be quantified according to both the shape of the                     layer, six nodes in the first hidden layer, five nodes in the
corresponding peak and its height. For an image, when                second hidden layer and one single node in the output layer.
using a multiresolution scheme for a dyadic standard                           Each layer is fully connected to the succeeding
decomposition of a function into sub-bands a filter bank             layer. The outputs of nodes of one layer are transmitted to
with a power of two number of filters should be used. When           nodes in another layer through links. The structure of an
using orthogonal wavelets like ones, one can easily simplify         ANN is shown in Figure 10 where the Energy maps are fed
the problem by gathering the channels by scale in both               as inputs into the trained neural network and the surface
directions. This process applied to a discrete wavelet is            roughness parameter (Rt) is estimated . In the training
called the scaled DWT. The frequency normalization can               phase, the desired value of the node in the output layer is
then be performed based on these filters.                            the actual roughness value, Rt obtained by stylus method.
                                                                     The ANN adjusts the weights in all connecting links such
                                                                     that the mean square error, i.e. the averaged squared error

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between the network output and the desired output is
minimized. Training of ANN is stopped as soon as the
specified number of epochs has reached and the values of
weights corresponding to the minimum error are restored.                                                                   … (14)
Once trained, the ANN is then tested for different sets of
input data. In the testing phase of the neural network, the
predicted roughness, Rt is the value of the node in the
output layer.
                                                                                                                           … (15)



                                                                                                                           … (16)




                                                                                                                            … (17)
Fig. 10 The System architecture of ANN used for predicting
                                                                     In Figure 12, f(x,y) is the highest resolution representation
                     Ra for surfaces
                                                                     of the image being transformed. It serves as the input for
                                                                     the first iteration and for the succeeding iterations; the
             VI. RESULTS AND DISCUSSION                              approximation coefficients Wφ (j, m, n) are given as input to
                                                                     the filter bank, to obtain the next set of wavelet coefficients.
Case 1: Feature Extraction using Scaled DWT

The blocks contain time reversed scaling and wavelet
vectors. The hφ (-n) and hΨ (-m) are low pass and high pass
decomposition filters. Blocks are containing a down arrow
and represent down sampling extracting every other point
from a sequence of points. Each pass through the filter bank
in Figure 11 decomposes the input signal into four lower
resolutions (or lower scale) components. The Wφ                       Fig. 12 Sub-band image decomposition for wavelet based
coefficients are created by two low pass (hφ based) filters                              feature extraction
and are thus called the approximation coefficients and {Wφ i
for i = H, V, D} are the horizontal, vertical and diagonal
detail coefficients.                                                 Thus the energy for each subband is calculated up to 4
                                                                     levels of decomposition and the image features Et, Eh, Ev
                                                                     and Ed are obtained from the energy map which is
                                                                     determined using tree-structured wavelet transform for each
                                                                     image. Few Sample enhanced machine images [Figure
                                                                     13(a) to 18(a)] are applied with DWT and the respective
                                                                     transform outcomes are shown in [Figure 13(b) to 18(b)]
                                                                     along with the energy details in Table 1.




               Fig. 11 2D DWT filter bank

Mathematically, the series of filtering and down sampling
operations are used to compute the DWT coefficients Wφ
(j,m,n) and {Wφi (j,m,n) for i = H,V,D} at scale j.                                           Figure 13(a)




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                                                                                  Figure 16(a)

Figure 13(b) Transform absolute coefficient




                                                                 Figure 16(b) Transform absolute coefficient


               Figure 14(a)




                                                                                  Figure 17(a).

Figure 14(b) Transform absolute coefficient




               Figure 15(a).                                     Figure 17(b) Transform absolute coefficient




                                                                                  Figure 18(a)
Figure 15(b) Transform absolute coefficient




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                                                                         Table 2 ANN estimated Rt for milling parameters (Image
                                                                        enhancement done and image features extracted using FT)




         Figure 18(b) Transform absolute coefficient

         Table 1 Energy maps obtained from DWT
  Fig.        Ea                Edetail Values
 Name      Values
                        Et       Eh        Ev  Ed
13(a)      99.0286 0.0396 0.1714 0.4482 0.3122

14(a)        99.0088    0.0204    0.1183    0.3862     0.4663

15(a)        97.7414    0.0272    0.2686    0.6214     1.3414

16(a)        98.5546    0.0393    0.3785    0.7579     0.2697

17(a)        98.5984    0.0606    0.2933    0.5217     0.5260           Table 3 ANN estimated Rt for milling parameters (Image
                                                                       enhancement done and image features extracted using WT)
18(a)        96.8104    0.0282    0.1311    0.5938     2.4364


Where Et is Energy total, Eh is Energy horizontal, Ev is
Energy Vertical and Ed is Energy diagonal. Ea is Energy
Approximation.

Case 2: Estimation of Rt using ANN
(a) For Milled surfaces

Two types of feature extraction and surface roughness
estimation using ANN is performed in this work. The first
one extracts the features using FT and the second uses the
WT. In FT approach the key input features collected for
training the network consist of
(i) average grey scale value (Ga)
(ii) major peak frequency (F1) and
(iii) Principal component magnitude squared value (F2).
The WT based feature extraction is already discussed in
case (i) of section VI. In the training phase (for both FT and
WT) the desired value of the node in the output layer is the
surface roughness Rt obtained using the stylus method. The
surface roughness Rt from ANN along with the stylus                    The results obtained are validated by plotting the
measurement values for the milled samples after image                  correlation graph between stylus measured (conventional
enhancement with FT (WT) extracted features is given in                method) Rr and vision measured (proposed) Rt for both the
Table 2 (Table 3).                                                     FT and WT techniques for milled components is shown in
                                                                       Figure 15.




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                                                                   Table 5 ANN estimated Rt for grinding parameters (Image
                                                                  enhancement done and image features extracted using WT)




Figure 15 Comparison between predicted roughness values
using vision approach and stylus approach for FT features
and WT features (milling)


(b) For grinding operations
The Rt value predicted using the trained ANN and that
measured using the stylus approach for the grinding
process after image enhancement with features extracted
using FT (WT) is given in Table 4 (Table 5).
                                                                  The results obtained are validated by plotting the
                                                                  correlation graph between stylus measured (conventional
                                                                  method) Rr and vision measured (proposed) Rt for both the
Table 4 ANN estimated Rt for grinding parameters (Image           FT and WT techniques for grinding components is shown
enhancement done and image features extracted using FT)           in Figure 16.




                                                                  Figure 16 Comparison between predicted roughness values
                                                                  using vision approach and stylus approach for FT features
                                                                  and WT features (grinding).

                                                                   VII. CONCLUSION AND FUTURE ENHANCEMENT.

                                                                           The developed model is tested online on images of
                                                                  specimens grabbed by computer vision systems with
                                                                  linearly decreasing intensity. The features of the grabbed
                                                                  enhanced image (to remove noise present in the captured
                                                                  image) are extracted using two different schemes, one using
                                                                  Fourier transform (FT) and the other using wavelet

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decomposition. The FT method is used to extract the                 [10] Daubechies, The wavelet transform, time-frequency
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[4] M.Y. Rafiq, G. Bugmann, D.J. Easterbrook, Neural                1. Mr. T.K.Thivakaran is presently a research scholar in
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[5] K. Venkata Ramana, B. Ramamoorthy, Statistical                  Professor in the faculty of Information Technology, Sri
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    of ASME, vol 125, Nov. 2003, pp. 844-852.                       University, Chidambaram. He has conducted workshops
[8] H.T. Hingle and J.H. Rakels, The practical application          and conferences in the area of Multimedia, Business
    of diffraction techniques to assess surface finish of           Intelligence, Analysis of Algorithms and Data Mining. He
    diamond turned parts, Ann. CARP, 32(1)(1983)499-                has presented and published more than 32 papers in
    501.                                                            conferences and journals and is the co-author of the book
[9] B. Josso, D.R. Burton, M.J. Lalor, Wavelet strategy for         Numerical Methods with C++ Program( PHI,2005). His
    surface roughness analysis and characterisation,                research interests include Data Mining, Algorithms, Image
    Comput. Methods Applications. Mech. Eng. 191 (8–                processing and Mobile Computing. He is life member of the
    10) (2001) 829–842.                                             Computer Society of India, Indian Society for Technical
                                                                    Education, Institute of Engineers etc.

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                                                                                              ISSN 1947-5500