An Approximated Box Height for Differential-Box-Counting Method to Estimate Fractal Dimensions of Gray-Scale Images

Problems of the Grid Size Selection in Differential Box-Counting (DBC) Methods and an Improvement Strategy

The differential box-counting (DBC) method is useful for determining the fractal dimension of grayscale images. It is simple to learn and implement and has been extensively utilized. However, this approach has several problems, such as over- or undercounting the number of boxes due to inappropriate parameter choices, limiting the calculation accuracy. Many studies have been conducted to increase the algorithm’s computational accuracy by improving the calculating parameters of the differential box-counting method. The grid size is a crucial parameter for the DBC method. Generally, there are two typical ways for selecting the grid size in relevant studies: consecutive integer and divisors of image size. However, both methods for grid size selection are problematic. The consecutive integer method cannot partition the image entirely and will result in the undercounting of boxes; the divisors of image size can partition the image completely. However, this method uses fewer grid sizes to compute fractal dimensions and has a relatively huge distance error (DE). To address the shortcomings of the above-mentioned two approaches, this research presents an improved grid size selection strategy. The improved method enhances computational accuracy by computing the discarded image edge areas in the consecutive integer method, allowing the original image information to be used as thoroughly as the divisor strategy. Based on fractional Brownian motion (FBM), Brodatz, and Aerials image sets, the accuracy of the three grid size selection techniques (consecutive integer method, divisors of image size method, and the improved algorithm) to compute the fractal dimension is then compared. The results reveal that, compared to the two prior techniques, the revised algorithm described in this study minimizes the distance error and increases the accuracy of the fractal dimension computation.

Hyperspectral Texture Metrology Based on Joint Probability of Spectral and Spatial Distribution

Texture characterization from the metrological point of view is addressed in order to establish a physically relevant and directly interpretable feature. In this regard, a generic formulation is proposed to simultaneously capture the spectral and spatial complexity in hyperspectral images. The feature, named relative spectral difference occurrence matrix (RSDOM) is thus constructed in a multireference, multidirectional, and multiscale context. As validation, its performance is assessed in three versatile tasks. In texture classification on HyTexiLa, content-based image retrieval (CBIR) on ICONES-HSI, and land cover classification on Salinas, RSDOM registers 98.5% accuracy, 80.3% precision (for the top 10 retrieved images), and 96.0% accuracy (after post-processing) respectively, outcompeting GLCM, Gabor filter, LBP, SVM, CCF, CNN, and GCN. Analysis shows the advantage of RSDOM in terms of feature size (a mere 126, 30, and 20 scalars using GMM in order of the three tasks) as well as metrological validity in texture representation regardless of the spectral range, resolution, and number of bands.

Multi-focus image fusion using fractal dimension

Multi-focus image fusion is defined as "the combination of a group of partially focused images of a same scene with the objective of producing a fully focused image." Normally, transform-domain-based image fusion methods preserve the textures and edges in the blend image, but many are translation variant. The translation-invariant transforms produce the same size approximation and detail images, which are more convenient to devise the fusion rules. In this work, a translation-invariant multi-focus image fusion approach using the à-trous wavelet transform is introduced, which uses fractal dimension as a clarity measure for the approximation coefficients and Otsu's threshold to fuse the detail coefficients. The subjective assessment of the proposed method is carried out using the fusion results of nine state-of-the-art methods. On the other hand, eight fusion quality metrics are considered for the objective assessment. The results of subjective and objective assessment on grayscale and color multi-focus image pairs illustrate that the proposed method is competitive and even better than some of the existing methods.