# A Multiscale Topographical Analysis Based on Morphological Information: The HEVC Multiscale Decomposition

^{1}

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Surface Processing

#### 2.1.1. Surface Texturing

_{2}O

_{3}) with 5 different increasing pressures P

_{i}(P

_{1}= 5 bars and P

_{5}= 6 bars). Sample 6 is the rod before sandblasting treatment. To practice morphological measurements, rods are then cut every 10 cm to obtain a sample of 1 cm (ten samples by rod). To evaluate the texturing process repeatability, 2 rods are investigated for each process condition, leading to 6 × 2 × 10 = 120 surface topographies for future investigations.

#### 2.1.2. Topographical Measurements

^{TM}, Middlefield, OH, USA) with magnification 50× (Figure 1a). The idea of light interferometer is based on using the wave properties of light to generate the 3D topography precisely [19]. It uses a scanning white light interferometry for producing surface row image and measuring the microstructure of surfaces in three dimensions: it measures the height (Z-axis) over an area with X and Y length and width [20]. To obtain a representative surface area, the stitching method (Figure 1c) processes with 20% overlap (135 topographical maps with 640 × 480-pixel resolution of each individual map; see (Table 1)). Finally, for each of the 120 investigated surfaces, a 13,952 × 2014 approximately 30 mega pixels map is analyzed on an area of 6.16 mm × 0.89 mm (Figure 1b) with a lateral resolution of 0.44 µm. A primary study based on topographical map segmentation has shown that these conditions allow for the detection of 2000 fine craters on the investigated surface due to the sandblasting process.

#### 2.1.3. Surface Pretreatment

^{2}area (these extractions allow for the division of each rectangular map into 7 squared maps that will allow for quantification of the uncertainties of the original map). After that, the topographical map is converted into a grey map with 16 bit-depth (Figure 2f). To obtain this transformation, the amplitude is normalized by the ratio of Sz (roughness parameter which represents the maximum amplitude of the surface topography). This transformation makes it possible to free oneself from the amplitude of the roughness in order to consider only the information contained in the topography. The amplitude parameter Rz can then be introduced later in the classification analysis, thus decorrelating the spatial information from the roughness amplitude.

#### 2.1.4. Multiscale Roughness Analysis

#### 2.2. Topographical Materials Texture Image Data Set

#### 2.3. Topographical Analysis from the GPS ISO 25178 Standard Using SVM Decomposition

**Set 1.**a single parameter, Sa, the most used parameters in surface topography;

**Set 2.**a set of Sa parameters computed at 30 different cutoff filters for LP, HP, and BP Gaussian filters;

**Set 3.**34 roughness parameters defined by the International Standard GPS ISO 25178 (Geometrical Product Specification); and

**Set 4.**34 roughness parameters defined by the International Standard GPS ISO 25178 (Geometrical Product Specification) computed at 30 different cutoff filters for LP, HP, and BP Gaussian filters.

#### 2.4. Information, Lossless Compression, and Topographical Caracterisation

## 3. Description of the Proposed Algorithm

#### 3.1. HEVC Intra-Prediction Coding

- HEVC Main 4:4:4 16 Still Picture (MSP) profile only considers intra-coding;
- Main-RExt (main_444_16_intra) and High Throughput 4:4:4 16 Intra apply both intra- and inter-coding.

#### 3.2. HEVC IPHM-Based Classification

- -
- Compress the entire topographical image database with HEVC lossless intra-prediction coding by computing the 35 intra-prediction modes for Prediction Units (PU) of size 4 × 4 pixels.
- -
- Search for the best prediction mode that minimizes the Sum of Absolute Difference (SAD). The selected mode indicates the relation between the pixels inside the Prediction Unit (PU) and the boundary neighbor pixels.
- -
- Count the frequently utilized prediction modes to arrange each mode in one histogram bin as given by the following equation:$${H}_{i}^{\prime}=\{{h}_{i}0\le i\le 34\}$$

#### 3.3. The Proposed Method

## 4. Simulation Results

#### 4.1. The Impact of Surface Topography Filtering Types on Achieved Compression Ratios

#### 4.2. Evaluating IPMH as Texture Feature Descriptor

#### 4.3. The Impact of Surface Topography Filtering Types on Topographical Images Classification Accuracy

- Case-1: the impact of considering the three-filtered image data sets together on the six surfaces categories’ classification performances.
- Case-2: the impact of each filter separately on the six surfaces categories’ classification performances.
- Case-3: the impact of each scale of analysis on the six surfaces categories’ classification performances.

#### 4.4. The Impact of Scale of Analysis on Topographical Images Classification Accuracy

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A. Analysis by Conventional Methods

**Table A1.**List of the 34 roughness parameters and their numerical values corresponding to the map of cable 5 (Figure A1).

ISO 25178 | |||

Height Parameters | |||

Sq | 6.42 | µm | Root-mean-square height |

Ssk | −0.468 | Skewness | |

Sku | 3.48 | Kurtosis | |

Sp | 18.8 | µm | Maximum peak height |

Sv | 29.0 | µm | Maximum pit height |

Sz | 47.8 | µm | Maximum height |

Sa | 5.04 | µm | Arithmetic mean height |

Functional Parameters (Volume) | |||

Vm | 0.243 | ${\mathrm{\mu}\mathrm{m}}^{3}/{\mathrm{\mu}\mathrm{m}}^{2}$ | Material volume |

Vv | 8.02 | ${\mathrm{\mu}\mathrm{m}}^{3}/{\mathrm{\mu}\mathrm{m}}^{2}$ | Void volume |

Vmp | 0.243 | ${\mathrm{\mu}\mathrm{m}}^{3}/{\mathrm{\mu}\mathrm{m}}^{2}$ | Peak material volume |

Vmc | 5.68 | ${\mathrm{\mu}\mathrm{m}}^{3}/{\mathrm{\mu}\mathrm{m}}^{2}$ | Core material volume |

Vvc | 7.13 | ${\mathrm{\mu}\mathrm{m}}^{3}/{\mathrm{\mu}\mathrm{m}}^{2}$ | Core void volume |

Vvv | 0.889 | ${\mathrm{\mu}\mathrm{m}}^{3}/{\mathrm{\mu}\mathrm{m}}^{2}$ | Pit void volume |

Functional Parameters (Stratified surfaces) | |||

Sk | 15.5 | µm | Core roughness depth |

Spk | 4.78 | µm | Reduced summit height |

Svk | 8.12 | µm | Reduced valley depth |

Smr1 | 8.62 | % | Upper bearing area |

Smr2 | 87.1 | % | Lower bearing area |

Spatial Parameters | |||

Sal | 26.6 | µm | Auto correlation length |

Str | 0.819 | Texture-aspect ratio | |

Feature Parameters | |||

Spd | 0.000312 | $1/\mathrm{\mu}{\mathrm{m}}^{2}$ | Density of peaks |

Spc | 0.306 | $1/\mathrm{\mu}\mathrm{m}$ | Arithmetic mean peak curvature |

S10z | 38.2 | µm | Ten-point height |

S5p | 15.4 | µm | Five-point peak height |

S5v | 22.7 | µm | Five-point pit height |

Sda | 2333 | µm | Mean dale area |

Sha | 3135 | µm | Mean hill area |

Sdv | 1745 | µm | Mean dale volume |

Shv | 1663 | µm | Mean hill volume |

EUR 15178N | |||

Hybrid Parameters | |||

Sdq | 0.981 | Root-mean-square slope | |

Sds | 0.00402 | $1/\mathrm{\mu}{\mathrm{m}}^{2}$ | Density of summits |

Ssc | 0.248 | $1/\mathrm{\mu}\mathrm{m}$ | Arithmetic mean summit curvature |

Sdr | 38.4 | % | Developed interfacial area |

Sfd | 2.51 | Fractal dimension of the surface |

**Method 1. Sa Analyses**. Sa is the arithmetic average value of roughness determined from deviations about the center plane. Sa is by far the most common roughness parameter, though this is often for historical reasons and not for particular merit, as the early roughness meters could only measure it. Whitehouse discusses the advantages of this parameter (robust and easy to understand) and the inconvenience (unable to characterize the skewness of the surface amplitude, i.e., difference of peaks and valleys, unable to characterize the size of peaks and valleys) [44]. The Sa is computed without filtering, i.e., at the whole scale. SVM classification is performed with this unique roughness parameter.**Method 2. Sa Multiscale Analysis**. As presented in Section 2.1, multiscale can be used to practice a multiscale decomposition and Sa roughness parameters are computed for all scales for the three Gaussian filters (pass band, low pass, and high pass). Giljean et al. [45] have shown that this multiscale analysis allows for the Sa roughness parameters to detect the size of the peaks and valleys, avoiding the main critic claimed by Whitehouse [44]. One obtains a set of parameters Sa (F,ε), where F is the filter and ε the scale length (cut off filter). From this set, SVM classification is processed.**Method 3. Whole-scale analysis by a set of roughness parameters.**Thirty-four R_{i}roughness parameters (see Table A1 for their descriptions) with i = {1, 2…,34} are computed without filtering, i.e., at the whole scale. Najjar et al. [46] has shown that the measure of functionality of a surface must be analyzed with the amplitude, spatial, and hybrid parameters to find the best one that characterizes the effect of roughness. They proposed a relevance function to classify the efficiency of roughness parameters based on variance analysis. One obtains a set of parameters R_{i}from which SVM classification is processed.**Method 4. Multiscale analysis by a set of roughness parameters.**Thirty-four R_{i}roughness parameters (see Table A1 for their descriptions) with i = {1, 2…,34} are computed for all scales for the three filters (pass band, low pass, and high pass). By analyzing all the roughness parameters of the GPS standard, Le Goic et. [10] showed that, with different types of filtering at different scales, ANOVA discriminates a wide range of tribological mechanisms by classification indexes based on databank of F values created from ANOVA [10]. One obtains a set of parameters Ri (F, ε), where F is the filter and ε is the scale length. From this set, SVM classification is processed.

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**Figure 1.**Measurements of rods on Zygo NewView 7300 (

**a**) with stitching method (

**c**) on a 6.16 mm × 0.89 mm area (

**b**).

**Figure 3.**Three-dimensional topography and motif maps with histograms of the height amplitudes (in µm) corresponding of the six process configurations.

**Figure 4.**The five topographies (

**1**–

**5**) obtained with different mechanical treatments applied on initial surface (

**6**).

**Figure 5.**High pass filtering with two cutoffs (8 and 78 µm) applied on the surfaces with two mechanical treatments, 1 and 4, and the initial surface, 6.

**Figure 6.**Low pass filtering with a cutoff of 78 µm applied on the surfaces with two mechanical treatments, 1 and 4, and the initial surface, 6.

**Figure 7.**Band pass filtering with cutoff of 440 µm applied on the surfaces with two mechanical treatments, 1 and 4, and the initial surface, 6.

**Figure 8.**One image (resolution of 1024 × 1024 pixels) from six mechanical material categories (1 to 6) with four different length scales and three filtering methods.

**Figure 9.**F median plots of the one factor ANOVA (factor: 6 surface categories) versus the scale (in µm) for the 3 filtering methods (band pass, high pass, and low pass).

**Figure 11.**Intra-prediction modes in High-efficiency video coding (HEVC) [29].

**Figure 12.**Illustrative example of HEVC intra-prediction efficiency: (

**a**) original image of 1024 × 1024 pixels; (

**b**) selected modes to predict the original image (each prediction mode is represented here by one among 35 different colors); (

**c**) intra-predicted image; and (

**d**) the residual image.

**Figure 13.**First five retrieved images for six images tests (categories 1 to 6) using Intra-Prediction Modes Histogram (IPMH) which indicate a classification accuracy of 20%.

**Figure 14.**Block diagram of the proposed model integrates the HEVC lossless intra prediction model with nonlinear support vector machine model.

**Figure 15.**Relationship between the scale of analysis and the six surface categories compression performance by using the multiscale low-pass (LP) data sets.

**Figure 16.**Relationship between the scale of analysis and the six surface categories’ compression performance by using the multiscale band-pass (BP) data sets.

**Figure 17.**Relationship between the scale of analysis and the six surface categories compression performance by using the multiscale high-pass (HP) data sets.

**Figure 18.**Illustrative example of HEVC intra-prediction efficiency for characterizing topographical image: (

**a**) original image of 1024 × 1024 pixels; (

**b**) selected modes to predict the original image (each prediction mode is represented here by one among 35 different colors); (

**c**) intra-predicted image; and (

**d**) the residual image (an anamorphic transformation is done on the whole gray scale to see morphological details).

**Figure 19.**Comparison between the IPMH averages for three different filtered image data sets: LP, BP, and HP data sets.

**Figure 20.**Block diagram depicting the procedure for learning and testing the support vector machine (SVM) model.

**Figure 21.**The topography classification performance of mixed three multiscale surface filtered image data sets: (

**a**) the effect of increasing the training set size on the classification accuracy and (

**b**) a confusion matrix for six surface category classifications by using 21% of the mixed data set for training.

**Figure 22.**The topographies classification performance of multiscale LP data set: (

**a**) the effect of increasing the training set size on the classification accuracy and (

**b**) a confusion matrix for six surface category classifications by using 42% of the LP data set for training.

**Figure 23.**The topographies classification performance of the multiscale BP data set: (

**a**) the effect of increasing the training set size on the classification accuracy and (

**b**) a confusion matrix for six surface category classifications by using 28% of the BP data set for training.

**Figure 24.**The topographies classification performance of the multiscale HP data set: (

**a**) the effect of increasing the training set size on the classification accuracy and (

**b**) a confusion matrix for six surface category classifications by using 35% of the HP data set for training.

**Figure 25.**Comparison between the achieved accuracy averages for three different filtered image data sets: LP, BP, and HP data set at all available scales of analysis.

**Figure 26.**The impact of scale of analysis on the performances of a compressed-domain classifier: (

**a**) the relation between the scale of analysis and the six surface categories’ compression and classification performances by using the multiscale LP data sets and (

**b**) a confusion matrix for six surface category. classifications by using 50% of the highest-scale LP data set for training.

**Figure 27.**The impact of scale of analysis on the performances of a compressed-domain classifier: (

**a**) the relation between the scale of analysis and the six surface categories’ compression and classification performances by using the multiscale BP data sets and (

**b**) a confusion matrix for six surface categories classification by using 50% of the highest-scale BP data set for training.

**Figure 28.**The impact of scale of analysis on the performances of a compressed-domain classifier: (

**a**) the relation between the scale of analysis and the six surface categories’ compression and classification performances by using the multiscale HP data sets and (

**b**) a confusion matrix for six surface categories classification by using 50% of the highest-scale HP data set for training.

Lens Magnification | 50× |
---|---|

Map resolution (pixel) | 640 × 480 |

Number of stitches | 5 × 27, 20% overlapping |

Final investigated area (mm) | 6.16 × 0.89 |

Lateral resolution (µm) | 0.44 |

Final resolution (pixel) | 13,952 × 2014 |

**Table 2.**Statistics of maximal F values for the three filtering methods (see Figure 9).

Filter | Scale | Fmean | F_{5}^{th} | F_{50}^{th} | F_{95}^{th} |
---|---|---|---|---|---|

Band pass | 78.2 | 566 | 441 | 558 | 721 |

High pass | 78.2 | 418 | 334 | 414 | 515 |

Low pass | 29.6 | 552 | 454 | 548 | 666 |

Coding Options | Chosen Parameter |
---|---|

Encoder version | 16.12 |

Profile | Main-still-picture |

Internal bit depth | 8 |

Frames to be encoded | 1 |

Max CU width | 16 |

Max CU height | 16 |

GOP | 1 |

Search range | 64 |

Quantization parameter | 0 |

Transform skip | Disabled |

Transform skip Fast | Disabled |

Deblocking filter | 0 |

Sample adaptive offset | Disabled |

Trans quant bypass ena | 0 |

CU Trans quant bypass | 0 |

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## Share and Cite

**MDPI and ACS Style**

Eseholi, T.; Coudoux, F.-X.; Corlay, P.; Sadli, R.; Bigerelle, M.
A Multiscale Topographical Analysis Based on Morphological Information: The HEVC Multiscale Decomposition. *Materials* **2020**, *13*, 5582.
https://doi.org/10.3390/ma13235582

**AMA Style**

Eseholi T, Coudoux F-X, Corlay P, Sadli R, Bigerelle M.
A Multiscale Topographical Analysis Based on Morphological Information: The HEVC Multiscale Decomposition. *Materials*. 2020; 13(23):5582.
https://doi.org/10.3390/ma13235582

**Chicago/Turabian Style**

Eseholi, Tarek, François-Xavier Coudoux, Patrick Corlay, Rahmad Sadli, and Maxence Bigerelle.
2020. "A Multiscale Topographical Analysis Based on Morphological Information: The HEVC Multiscale Decomposition" *Materials* 13, no. 23: 5582.
https://doi.org/10.3390/ma13235582