Fast Color Quantization by K-Means Clustering Combined with Image Sampling

Frackiewicz, Mariusz; Mandrella, Aron; Palus, Henryk

doi:10.3390/sym11080963

Cited by 10 publications

(5 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This algorithmic approach is necessary as there is no explicit minimum of L θ (h, •). Let us stress that, while Monte Carlo approaches and other dithering methods have historically contributed to the image quantization problem, the last two decades were marked by more evolved developments, using adaptive kernels [33] and clustering algorithms [34,35]. Here, for the sake of physical interpretation, we focus our attention on the classic Monte Carlo approach as it contains the minimal ingredients to tackle this problem.…”

Section: Monte Carlo Image Generationmentioning

confidence: 99%

“…considering alternatives to the Euclidean distance such as perception based cost functions [33], structural similarity metrics [37], quality indices [35], distances including transport terms [43] or edge detection [33], which take into account a priori the local arrangement of the pixels. within the Econophysics & Complex Systems Research Chair, under the aegis of the Fondation du Risque, the Fondation de l'Ecole polytechnique, the Ecole polytechnique and Capital Fund Management.…”

Section: J Stat Mech (2023) 033401mentioning

confidence: 99%

See 1 more Smart Citation

A new spin on color quantization

2023

View full text Add to dashboard Cite

We address the problem of image color quantization using a maximum entropy based approach. Focusing on pixel mapping we argue that adding thermal noise to the system yields better visual impressions than that obtained from a simple energy minimization. To quantify this observation, we introduce the coarse-grained quantization error, and seek the optimal temperature which minimizes this new observable. By comparing images with different structural properties, we show that the optimal temperature is a good proxy for complexity at different scales. Noting that the convoluted error is a key observable, we directly minimize it using a Monte Carlo algorithm to generate a new series of quantized images. Adopting an original approach based on the informativity of finite size samples, we are able to determine the optimal convolution parameter leading to the best visuals. Finally, we test the robustness of our method against changes in image type, color palette and convolution kernel.

show abstract

Section: Monte Carlo Image Generationmentioning

confidence: 99%

Section: J Stat Mech (2023) 033401mentioning

confidence: 99%

A new spin on color quantization

2023

View full text Add to dashboard Cite

show abstract

“…The simplicity of Lloyd's procedure enables us to apply it to a wide range of problems, including face detection, image segmentation, signal processing and many others [92]. Frackiewicz et al [93] presented a color quantization method based on downsampling of the original image and k-means clustering on a downsampled image. The k-means clustering algorithm used in [94] was proposed for identifying electrical equipment of a smart building.…”

Section: Algorithm 1 Lloyd(s)mentioning

confidence: 99%

Self-Adjusting Variable Neighborhood Search Algorithm for Near-Optimal k-Means Clustering

Kazakovtsev¹,

Rozhnov²,

Popov³

et al. 2020

Computation

View full text Add to dashboard Cite

The k-means problem is one of the most popular models in cluster analysis that minimizes the sum of the squared distances from clustered objects to the sought cluster centers (centroids). The simplicity of its algorithmic implementation encourages researchers to apply it in a variety of engineering and scientific branches. Nevertheless, the problem is proven to be NP-hard which makes exact algorithms inapplicable for large scale problems, and the simplest and most popular algorithms result in very poor values of the squared distances sum. If a problem must be solved within a limited time with the maximum accuracy, which would be difficult to improve using known methods without increasing computational costs, the variable neighborhood search (VNS) algorithms, which search in randomized neighborhoods formed by the application of greedy agglomerative procedures, are competitive. In this article, we investigate the influence of the most important parameter of such neighborhoods on the computational efficiency and propose a new VNS-based algorithm (solver), implemented on the graphics processing unit (GPU), which adjusts this parameter. Benchmarking on data sets composed of up to millions of objects demonstrates the advantage of the new algorithm in comparison with known local search algorithms, within a fixed time, allowing for online computation.

show abstract

“…An efficient color quantization approach on the basis of modified K-means clustering is put forward in this study. The high complexity of the computation of K-means arises from the requirement to make a lot of comparisons of the original data 9 . Therefore, the method we presented samples pixels with distinctive colors that decrease the data for clustering operation, which will greatly reduce the data processing time.…”

Section: Introductionmentioning

confidence: 99%

Fast image quantization with efficient color clustering (Retraction Notice)

Liu

2023

International Workshop on Frontiers of Graphics and Image Processing (FGIP 2022)

View full text Add to dashboard Cite

Color image quantization has been widely used as an important task in graphics manipulation and image processing. The key to color image quantization is to generate an efficient color palette. At present, there are many color image quantization methods that have been presented, which are fundamentally clustering-based algorithms. As an illustration, the K-means clustering algorithm is quite popular. However, the K-means algorithm has not been given sufficient focus in the field of color quantization due to its high computational effort caused by multiple iterations and its very susceptibility to initialization. This paper presented an efficient color clustering method to implement fast color quantization. This method mainly addresses the drawbacks of the conventional K-means clustering algorithm, which involves reducing the data samples and making use of triangular inequalities to accelerate the nearest neighbor search. The method mainly contains two stages. During the first phase, an initial palette is generated. In the second phase, quantized images are generated by a modified K-means method. Major modifications include data sampling and mean sorting, avoiding traversal of all cluster centers, and speeding up the time to search the palette. The experimental results illustrate that this presented method is quite competitive with previously presented color quantization algorithms both in the matter of efficiency and effectiveness.

show abstract

Fast Color Quantization by K-Means Clustering Combined with Image Sampling

Cited by 10 publications

References 16 publications

A new spin on color quantization

A new spin on color quantization

Self-Adjusting Variable Neighborhood Search Algorithm for Near-Optimal k-Means Clustering

Fast image quantization with efficient color clustering (Retraction Notice)

Contact Info

Product

Resources

About