Detection of anisotropy of friction surface images Zbigniew Rudnicki, dr inż., Marek Mruk, mgr Computer Methods and Systems, XI.2007, Krakow

2 Introduction Processes of friction and corresponding wear very often cause: changes of surface anisotropy. The paper describes application of computer image analysis for friction surface state inspection by: - measuring of surface image anisotropy

3 Changes of surface anisotropy The wear process can cause: –increase of anisotropy or –decrease of anisotropy depending on initial state of surface.

4 Example 1. Decrease of anisotropy - caused by wear

5 Example 2. Increase of anisotropy - caused by wear of cross-hatch finished surface of Perkins tractor machine cylinder

6 The Goal of research Verification of usability of some image features - which are often used in gray texture image analysis - for measuring of the anisotropy and directionality in friction surface images

7 Anisotropy of image feature. Definitions: The investigated feature C possesses an anisotropy when the values of this feature depends relevantly on the scanning angle  (or image rotation angle -  ): C(  const The anisotropy measure An(C) of the feature C(  is defined as: An(C) = 1 - min(C(  ) / max(C(  )

8 The main direction of image feature If the function C(  has the global maximum for angle  so this angle designates the main direction of this feature and the image possesses directionality on account of the feature C If more than one local maximum of C(  is significant - so more than one direction can be taken into consideration.

9 The main steps of the research: A) Investigation of selected image features on the base of several pattern images, for working out the best method of detection and measuring of anisotropy and directionality B) Measuring of anisotropy and directionality for some classes of real images - as the test of proposed method.

10 Subtopics in step A:  Selecting the feature which is the most sensitive on image anisotropy  Defining: the measure of image anisotropy for selected feature, and the main direction of image  Feature standarization to range [0; 1] and to make independence on image size  Working out computer programs for: –Inspection (by graphs) of feature dependence on skanning angle –Measurement of anisotropy –Measurement or main direction and the second direction (if exists)

11 A) Tested pattern images. and rotation of image

12 Skanning angle and rotation of images The skanning angle was:  0 o for all features which were extracted. For evaluation C(  ) - instead of changing  the sequence of image rotations by angle  was applied:  = 0 o, -5 o, -10 o,..., -180 o. So the result was the same as for:  0 o, 5 o, 10 o,..., 180 o

13 Features from: “Run Length Matrix” R All investigated features were calculated from: Run Length Matrix: R Matrix R is obtained for given scanning angle  The value of matrix element R g,j gives information: - how many “runs” of length j and gray level g there were in the image. The size of matrix R are Lg x Lr where: Lr - maximal length of run (in pixels) Lg - number of gray levels.

14 The features calculating from matrix R: (1) Short Run Emphasis inverse moment „Odwrotny moment uwydatnienia krótkich pasm” (2) Long Run Emphasis moment “Moment uwydatnienia długich pasm” (3) Run Length Nonuniformity “Niejednorodność pasm” (4) Fraction of image in runs „Część obrazu w pasmach”

15 The features calculating from matrix R: (1) (2) (3) (4) where: Lk = number of columns in image (or pixels in row), N = number of all pixels,

16 Feature standarization - to range [0;1] (gives independence on image size) Only the features LngRemph and RLNonUni need standarization : (2a) (3a)

17 Redefinition of investigated features Only the feature LRE has maximum for main direction of texture and other features has minimum for this direction so they was redefined. Finally - the four investigated features were: C1(  ) = 1-SRE(  ), C2(  ) = LRE(  ), C3(  ) = 1-RLN(  ), C4(  ) = 1-FIR(  ).

18 The results for pattern image 1: 255 gray levels

19 The results for pattern image 2: Only 3 gray levels: 0, 120, 240

20 The results for pattern image 3: Before correction After correction

21 The results for real images (1): „New” „Wear”

22 Image feature LRE anisotropy for 2 classes of images (1)

23 The results for real images (2):

24 Image feature LRE anisotropy for 2 classes of images (2) surfaces of Perkins machine cylinders:

25 LRE discrimination ability - Fisher’s coefficient: Where:  - mean V - variance

26 Summary The feature: Long Run Emphasis Moment was standarized - as LRE - and selected as the best feature for measurement of image anisotropy The measure of anisotropy on the basis of this feature was defined Many computer programs in Matlab were worked out for analysis of anisotropy (as function of scanning angle) and evaluation of image directionality These programs were applied with success not only for pattern images but to some classes of real images too.

27 Thank you for attention !