There is a growing interest in cultural heritage preservation. The notion of HyperHeritage highlights the creation of new means of communication for the perception and data processing in cultural heritage. This article presents the Digital Surface HyperHeritage approach, an academic project to identify the topography of art painting surfaces at the scale at which the elementary information of sensorial rendering is contained. High-resolution roughness and imaging measurement tools are then required. The high-resolution digital model of painted surfaces provides a solid foundation for artwork-related information and is a source of many potential opportunities in the fields of identification, conservation, and restoration. It can facilitate the determination of the operations used by the artist in the creative process and allow art historians to define, for instance, the meaning, provenance, or authorship of a masterpiece. The Digital Surface HyperHeritage approach also includes the development of a database for archiving and sharing the topographic signature of a painting.

There is a growing demand for high level surface characterization. The functionality of machine parts, such as tribological behavior, depends on the texture of contacting surfaces. The relation between texture parameters depending on the scaling of texture features, finishing process parameters, such as grain sizes for grinding, and functionality of a surface is investigated. Due to the fractal aspect of the studied surfaces, more advanced tools are used for characterization. This article presents a comparison of three different segmentation methods (patchwork, box, and motif) for multiscale decomposition, using different roughness parameters to analyse the texture of polymer samples finished with various abrasive papers from FEPA grade 80 to 4000 to represent varying abrasion on the different scales. The consistencies and discrepancies of the different procedures of multiscale decomposition in the relation between separability of macro and micro abrasions, identification of self-similarity and features or regions on varying scales and the finishing with different abrasive grain sizes have been investigated.

Identification of an individual artist’s touch on paintings is studied using surface metrology. Paintings’ topographies were measured using focus variation and stitching, creating 13 × 13 mm maps with 1 μm sampling intervals, and 169 megapixels, with a 10X objective lens. Topographic characterization parameters were analyzed for their ability to differentiate different painters’ renderings. Statistical treatments from data mining were used to discriminate, by optimization, multiscale topographic signatures characterized by a multitude of areal texture parameters. It appears that a fractal dimension can define 3 characteristic scale ranges. One from 3 to 70 μm corresponds to brushstroke details. Another, from 70 to 700 μm, corresponds to the topography of the material of the canvas fabric. Finally, scales greater than 700 μm correspond to undulations of the canvas. For scales less than 50 μm, the fractal structure of the topography left by brushstrokes follows a power law characterized by the slopes of the topography. The topography of the clouds painted on the canvas has an Sdq (topographic slopes) increasing with the clarity of the clouds at scales of 3–500 μm. According to the Torrance-Sparrow theory, the higher the Sdq, the more diffuse the light on the surface. The painter therefore wanted to show, by his brushstroke, that the light clouds diffuse more light giving an impression of local brightness. This study is confirmed by the analysis of the painting of Max Savy, a French painter from Carcassonne (1918–2009), which was measured with a white light interferometer Zygo NewView 7300, a X100 objective lens giving a 517 μm × 517 μm stitched surface, with a sampling interval of 0.109 μm. The box-counting method for estimating the fractal dimension of the topography of an oil painting appears optimal by the fact that it morphologically integrates scale variations of the local slopes of the surface morphology. This method thus characterizes the multiscale aspects, as well as the scale changes, of the topography.

Surface topography is an efficient tool for the understanding of physical phenomena, especially if multiscale roughness analysis is performed. However, the observable scale range in a topography measured with 3D optical profilometers is quite limited. Therefore, all scales linked to a physical phenomenon might not be measured, which impedes the correct analysis of the surface. Stitching of 3D topographies, a technique combining elementary topographic maps into a larger one, can be used to increase the scale range for an objective lens. A high resolution over a large field of measurement topography is then generated. A literature review of 3D topography stitching algorithm highlights the stitching procedure, and detailed explanations on in-plane registration algorithms are provided. However, some existing 3D topography stitching algorithms are not sufficiently accurate for the registration of surface, especially at smaller scales. This paper proposes a new reflectance-based multimap 3D stitching algorithm and three of its variants. These algorithm variants are compared to three existing 3D stitching algorithms (geometric, cross-correlation and global optimization of differences) on four test cases, containing measured elementary topographic maps obtained on four surfaces and with four 3D optical profilometers (two focus variation microscopes and two interferometers). Five qualitative and quantitative criteria and indicators are proposed for the comparison of 3D topography stitching algorithms: visual inspection, run time, memory usage, mean repositioning error and stitching error estimator. Lastly, two quantitative indicators and criteria are new indicators proposed in this article. Overall, the new 3D stitching algorithms based on reflectance and multimaps have a lower mean repositioning error and stitching error estimator compared to other existing algorithms. This highlights the relevance of multimap stitching algorithms in the case of 3D topographies. A new decision-helping tool, the stitching gain lift plot (SGL plot), is described for the selection of the best stitching algorithm for a given test case. The SGL plot especially highlights the higher performance of two of the variants of the novel algorithm compared to the three existing 3D stitching algorithms.

Various methods exist for multiscale characterization of surface topographies, each offering unique insights and applications. The study focuses on fractal-based approaches, distinguishing themselves by leveraging fractals to analyze surface complexity. Specifically, the Richardson Patchwork method, used in the ASME B46.1 and ISO 25178 standards, is compared to the Sdr parameter derived from ISO 25178-2, with a low-pass Gaussian filter for multiscale characterization. The comparison is performed from the relative area calculated on topographies of TA6V samples grit blasted with different pressures and blasting materials (media). The surfaces obtained by grit blasting have fractal-like characteristics over the scales studied, enabling the analysis of area development at multiple levels based on pressure and media. The relative area is similar for both methods, regardless of the complexity of the topographies. The relevance scale for each calculation method that significantly represents the effect of grit blasting pressure on the increased value of the relative area is a tiling of 7657.64 µm² of triangle area for the Patchwork method and a 124.6 µm cut-off for the low-pass Gaussian filter of the Sdr method. These results could facilitate a standard, friendly, new fractal method for multiscale characterization of the relative area.