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In this paper, we propose a complete framework to process images captured under uncontrolled lighting and especially under low lighting. By taking advantage of the Logarithmic Image Processing (LIP) context, we study two novel functional…
Aspl{\"u}nd's metric, which is useful for pattern matching, consists in a double-sided probing, i.e. the over-graph and the sub-graph of a function are probed jointly. It has previously been defined for grey-scale images using the…
We establish the link between Mathematical Morphology and the map of Asplund's distances between a probe and a grey scale function, using the Logarithmic Image Processing scalar multiplication. We demonstrate that the map is the logarithm…
Aspl\"und 's metric, which is useful for pattern matching, consists in a double-sided probing, i.e. the over-graph and the sub-graph of a function are probed jointly. This paper extends the Aspl\"und 's metric we previously defined for…
We introduce a simple expression for the map of Asplund's distances with the multiplicative Logarithmic Image Processing (LIP) law. It is a difference between a morphological dilation and a morphological erosion with an additive structuring…
A new set of mathematical morphology (MM) operators adaptive to illumination changes caused by variation of exposure time or light intensity is defined thanks to the Logarithmic Image Processing (LIP) model. This model based on the physics…
Measuring perceptual similarity is a key tool in computer vision. In recent years perceptual metrics based on features extracted from neural networks with large and diverse training sets, e.g. CLIP, have become popular. At the same time,…
Similarity metrics have played a significant role in computer vision to capture the underlying semantics of images. In recent years, advanced similarity metrics, such as the Learned Perceptual Image Patch Similarity (LPIPS), have emerged.…
In order to create an image segmentation method robust to lighting changes, two novel homogeneity criteria of an image region were studied. Both were defined using the Logarithmic Image Processing (LIP) framework whose laws model lighting…
In Mathematical Morphology for grey-level functions, an image is analysed by another image named the structuring function. This structuring function is translated over the image domain and summed to the image. However, in an image…
Multidimensional projections (MP) are among the most essential approaches in the visual analysis of multidimensional data. It transforms multidimensional data into two-dimensional representations that may be shown as scatter plots while…
In the framework of Asplund spaces, we use two equivalent instruments - rich families and suitable models from logic - for performing separable reductions of various statements on Frechet subdifferentiability of functions. This way,…
In the literature, several studies have shown that state-of-the-art image similarity metrics are not perceptual metrics; moreover, they have difficulty evaluating images, especially when texture distortion is also present. In this work, we…
Two objects may be close in the Hausdorff metric, yet have very different geometric and topological properties. We examine other methods of comparing digital images such that objects close in each of these measures have some similar…
The well-aligned attribute of CLIP-based models enables its effective application like CLIPscore as a widely adopted image quality assessment metric. However, such a CLIP-based metric is vulnerable for its delicate multimodal alignment. In…
Given a closed orientable surface (\Sigma) of genus at least two, we establish an affine isomorphism between the convex compact set of isotopy-invariant topological measures on (\Sigma) and the convex compact set of additive functions on…
Deep learning-based bilateral grid processing has emerged as a promising solution for image enhancement, inherently encoding spatial and intensity information while enabling efficient full-resolution processing through slicing operations.…
Data consisting of a graph with a function mapping into $\mathbb{R}^d$ arise in many data applications, encompassing structures such as Reeb graphs, geometric graphs, and knot embeddings. As such, the ability to compare and cluster such…
We analyze invariant measures of two coupled piecewise linear and everywhere expanding maps on the synchronization manifold. We observe that though the individual maps have simple and smooth functions as their stationary densities, they…
We first consider interval partitions whose complements are Lebesgue-null and introduce a complete metric that induces the same topology as the Hausdorff distance (between complements). This is done using correspondences between intervals.…