Guided image filter
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This document discusses guided image filtering. It introduces the guided filter, which performs edge-preserving smoothing while maintaining the gradient of a guidance image. The guided filter works by assuming a local linear model between the guidance image and filtering output within a window, and solving a cost function to determine the filter coefficients. It can perform edge-preserving smoothing and gradient-preserving filtering in linear time complexity.
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Abstract We propose a new generalized algorithm using the exploratory data model as unified frame work. Enhancement of contrast and sharpness of an image is required in many applications. In applications like medical radiography enhancing movie features and observing the planets it is necessary to enhance the contrast and sharpness of an image. Unsharp masking is good tool for sharpness enhancement; it is an anti blurring filter. By using unsharp masking algorithm for sharpness enhancement, the resultant image suffering with two problems, first one is a hallo is appear around the edges of an image, and second one is rescaling process is needed for the resultant image. The aim of this paper is to enhance the contrast and sharpness of an image simultaneously and to solve the problems. In the proposed algorithm, we can adjust the two parameters controlling the contrast and sharpness to produce the desired output. The proposed algorithm is designed to address issues:1) simultaneously enhancing contrast and sharpness by means of individual treatment of the model component and the residual,2)reducing the halo effect by means of an edge-preserving filter using Bilateral filter. Experimental results, which comparable to recent published results, shows that proposed algorithm is able to significantly improve the sharpness and contrast of an image. This makes the proposed algorithm practically useful. Index Terms: Bilateral filter, edge-preserving filter, exploratory data model, Image Enhancement, Unsharp Masking
New approach for generalised unsharp masking alogorithm
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
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Convolutional Neural Networks CNN
Convolutional neural network (CNN) is a regularized type of feed-forward neural network that learns feature engineering by itself via filters (or kernel) optimization. Vanishing gradients and exploding gradients, seen during backpropagation in earlier neural networks, are prevented by using regularized weights over fewer connections. For example, for each neuron in the fully-connected layer 10,000 weights would be required for processing an image sized 100 × 100 pixels. However, applying cascaded convolution (or cross-correlation) kernels, only 25 neurons are required to process 5x5-sized tiles. Higher-layer features are extracted from wider context windows, compared to lower-layer features.
CNNs are also known as Shift Invariant or Space Invariant Artificial Neural Networks (SIANN), based on the shared-weight architecture of the convolution kernels or filters that slide along input features and provide translation-equivariant responses known as feature maps. Counter-intuitively, most convolutional neural networks are not invariant to translation, due to the downsampling operation they apply to the input.
Feed-forward neural networks are usually fully connected networks, that is, each neuron in one layer is connected to all neurons in the next layer. The "full connectivity" of these networks make them prone to overfitting data. Typical ways of regularization, or preventing overfitting, include: penalizing parameters during training (such as weight decay) or trimming connectivity (skipped connections, dropout, etc.) Robust datasets also increases the probability that CNNs will learn the generalized principles that characterize a given dataset rather than the biases of a poorly-populated set.
Convolutional networks were inspired by biological processes in that the connectivity pattern between neurons resembles the organization of the animal visual cortex. Individual cortical neurons respond to stimuli only in a restricted region of the visual field known as the receptive field. The receptive fields of different neurons partially overlap such that they cover the entire visual field.
CNNs use relatively little pre-processing compared to other image classification algorithms. This means that the network learns to optimize the filters (or kernels) through automated learning, whereas in traditional algorithms these filters are hand-engineered. This independence from prior knowledge and human intervention in feature extraction is a major advantage.
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Guided image filter
- 1. Guided Image Filtering HyeongJun Kwon 2019-2
- 2. Contents 2 1. Introduction 2. Overall Framework 3. Guided Filter 4. Computation and Efficiency
- 3. Guided Image Filtering 3 Introduction Bileteral filter issue 1. Gradient Reversal 2. Computatonal complexity 𝒪 𝑁𝑟2 with kernel radius 𝑟
- 4. Guided Image Filtering 4 Overall framework
- 5. Guided Image Filtering 5 Guided Filter Filtering output Bilateral filter Definition Assume the guided filter is a local linear model between the guidance I and the filtering output q
- 6. Guided Image Filtering 6 Guided Filter Definition Assume the guided filter is a local linear model between the guidance I and the filtering output q Constraints from p(input image) Cost function
- 7. Guided Image Filtering 7 Guided Filter Definition Solution 𝑤ℎ𝑒𝑟𝑒 𝑝 𝑘 = 1 𝑤 𝑖∈𝑤 𝑘 𝑝𝑖, μ 𝑘 and σ 𝑘 2 are the mean and variance of 𝐼
- 8. Guided Image Filtering 8 Guided Filter Definition Algorithm
- 9. Guided Image Filtering 9 Guided Filter Edge-Preserving Filtering Consider the case 𝐼 ≡ 𝑝. In this case 𝑎 𝑘 = σ 𝑘 2 / σ 𝑘 2 + ϵ and 𝑏 𝑘 = 1 − 𝑎 𝑘 μ 𝑘 Image I changes a lot in window, σ 𝑘 2 ≫ ϵ, so ak ≈ 1 and bk ≈ 0 Case 1: High Variance Case 2: Flat Patch Image I is a almost a constant in window, σ 𝑘 2 ≪ ϵ, so ak ≈ 0 and bk ≈ 𝜇k
- 10. Guided Image Filtering 10 Guided Filter Filter Kernel Gaussian Weight
- 11. Guided Image Filtering 11 Guided Filter Gradient-Preserving Filtering 𝑎 𝑘 = σ 𝑘 2 σ 𝑘 2 + ϵ < 1 and 𝑏 𝑘 is a constant. So we have 𝜕xq = ak 𝜕xp 𝜕 𝑥 𝑑 = 𝜕 𝑥 𝑝 − 𝜕 𝑥 𝑞 = 1 − 𝑎 𝑘 𝜕 𝑥 𝑝
- 12. Guided Image Filtering 12 Guided Filter Gradient-Preserving Filtering
- 13. Guided Image Filtering 13 Guided Filter Gradient-Preserving Filtering
- 14. Guided Image Filtering 14 Computation and Efficiency Box filter algorithm
Editor's Notes
- Guided filter의 목적성과 전체 구조 그리고 method 마지막으로 computational efficiency에 대해 설명하겠습니다.
- Guided filter를 설명하기 전에 먼저 bilateral filter의 issue를 먼저 다루겠습니다. 두 가지 issue가 있는데 첫 번째는 edge 부근에서 경계선이 뒤집히는 gradient reversal effect랑 kerner radius r에 비례하여 증가하는 computational cost 문제가 있습니다. Guided filter는 이 두가지 문제를 해결하는 focus에 집중되어 있습니다.
- 전체 구조입니다. Guidance image를 활용하는 방식의 차이가 있다는 것을 확인할 수 있습니다.
- 논문의 첫 번째 식부터 살펴보면 가이던스 이미지를 기반으로 인풋 이미지를 weight sum을 하여 결과를 내는 것을 필터링 아웃풋이라 정의 합니다. Bilateral filter의 weight는 다음과 같습니다. 그러면 guided filter의 가정에 대해서 말하면 output과 guidance image와 linear하다고 가정을 합니다. W_k는 window 입니다.
- 또한, input image를 통해 constraints를 다음과 같이 주어서 (a_k, b_k)를 정의해 줄 입니다. 또한, cost function은 아웃풋과 인풋의 차이를 줄이는 것이 목적이며 epsilon은 a_k의 값이 커지는 것을 방지하는 regularized term입니다.
- Mu_k와 sigma^2은 guidance image의 평균과 분산입니다. A_k는 guidance image와 input image의 covariance를 통해 구해줍닏. 또한, b_k는 input image의 평균과 guidance image의 평균 그리고 a_k를 통해 구해줍니다.
- 전체 알고리즘 입니다.
- 어떻게 guided filter가 edge preserving을 하는지 설명하겠습니다. 만약 guidance image와 input image가 동일하다고 가정하면 a_k와 b_k는 다음과 같습니다. 이제 window 내에 edge가 있는 경우와 없는 경우를 비교해보면 첫 번쨰로 edge가 있는경우 그렇게 될 경우 image가 window 내에서 intensity의 큰 변화를 가진다는 의미와 동일하고(edge) 높은 분산을 가지게 됩니다. 이렇게 되면 분산은 epsilon보다 큰 값을 가지게 되고 이는 a_k는 약 1로 수렴합니다. 이는 아웃풋이미지와 가이던스 이미지가 리니어 하므로 input image의 값의 변화에 민감하게 반응을 한다는 것입니다. 두 번째로 edge가 없는 경우. 즉, window 내에 값의 큰 변화가 없는 경우 분산은 0에 가까워지고 a_k는 0에 수렴하므로 b_k가 mu에 가까워 지는데 이 mu는 guidance image의 평균이므로 mean filter 역할을 하게 됩니다. 이를 통해 edge에서는 edge를 preserving하는 방향으로 filter가 activate되고 반대에서는 mean filter가 activate 됩니다.
- Filter kernel은 다음과 같이 정의 되며 filter kernel은 output을 input으로 derivation한 값이고 증명은 따로 설명하지 않겠습니다. 다음은 gaussian weight로 다음 figure에서 기존의 guided filter는 x, y방면으로 더욱 activate되어 있는 것을 알 수 있습니다. 이를 해결하기 위해 gaussian weight를 곱해줘서 rotational assymetric 현상을 해결했습니다.
- Gradient reversal issue를 해결한 것을 확인해보겠습니다. Bilateral filter를 살펴보면 디테일을 위해 detail layer를 boost시키는데 base layer에 input layer보다 작아지는 pixel로 인해 gradient reversal effect가 생깁니다. 이는 pixel 근처에 비슷한 pixel이 존재하지 않으므로 인해 일어나는 문제이다. 다음 식을 살펴보면 a_k는 1 보다 작으므로 detail의 gradient가 edge 부근에서 reveral되는 경우가 줄어든다.
- Algorithm1은 Box filter algorithm이며 이는 N times algorithm인 것을 algorithm2 식을 통해 확인할 수 있습니다.