MTandHJ的博客

文章目录概主要内容求解相似度总的算法流程skimage.future.graph.cutShi J. and Malik J. Normalized cuts and image segmentation. In IEEE Transactions on Pattern Analysis and Machine Intelligence.概在Digital Image Preprocessing的书上看到了这个算法, 对于其公式结果的推出不是很理解, 于是下载下来看了看. 本文主要讲的是一种利用图

文章目录SLIC Superpixel algorithm距离函数的选择代码Gonzalez R. C. and Woods R. E. Digital Image Processing (Forth Edition).单个像素的意义其实很小, 于是有了superpixel的概念, 即一簇pixels的集合(且这堆pixels共用一个值), 这会导致图片有非常有趣的艺术风格(下图便是取不同的superpixel大小形成的效果, 有种抽象画的感觉?):经过superpixel的预处理后, 图片可以

文章目录代码skimage.transform.hough_line本来想偷懒不记录的, 但是这个Hough Transform实在是有趣.通过Canny算法等将edge的大体部分检测了出来, 但是往往这些检测出来的点并不是连续的, 那么怎么才能将这些点合理地连接在一起呢?这个Hough Transform就可以做到这一点. 首先需要明确的一点是, 我们应该将怎么样的点连接起来, 将其中空缺部分的点填补起来? 最简单但是也非常符合直观理解的便是当有多个点处于同一直线的时候, 我们就认为这条线在原图中其

文章目录概reflection and translationErosion and DilationErosion示例skimage.morphology.erosiondilation示例skimage.morphology.dilation对偶性Opening and ClosingOpening示例skimage.morphology.openingClosing示例skimage.morphology.closing对偶性The Hit-or-Miss Transform一些基本的操作Bounda

文章目录概主要内容Sermanet P., Eigen D., Zhang X., Mathieu M., Fergus R., LeCun Y. OverFeat:integrated recognition, localization and detection using convolutional networks. In International Conference on Learning Representations (ICLR), 2014.概通常的sliding window

文章目录Fourier Transform基本的定义性质对称性卷积FFTFourier Transform基本的定义严格来说, 傅里叶变换是Schwartz space 上的一一映射, 对于L1L^1L1, 即可积函数我们都可以找到其对应的傅里叶变换.符号定义傅里叶变换: f^(u)\hat{f}(u)f^​(u)∫−∞+∞f(t)e−j2πutdt\int_{-\infty}^{+\infty} f(t) e^{-j2\pi u t} \mathrm{d}t∫−∞+∞​f(t

文章目录Coding RedundancyHuffman CodingGolomb CodingArithmetic CodingLZW CodingRun-Length CodingSymbol-Based CodingBit-Plane CodingBlock Transform CodingTransform SelectionSubimage Size SelectionBit AllocationJPEGPredictive CodingOptimal PredictorsOptimal Quan

文章目录目标小波变换Scaling FunctionsWavelet Functions二者的联系离散的情形高效变换二维的情形示例目标首先, 既然是变换, 那么就是从一个域到另一个域, 即如下:f(x)=∑kcj0(k)φj0,k(x)+∑j=j0∞∑kdj(k)ψj,k(x),cj0=⟨f(x),φj0,k(x)⟩,dj=⟨f(x),ψj,k(x)⟩.f(x) = \sum_k c_{j_0} (k) \varphi_{j_0, k} (x) + \sum_{j=j_0}^{\infty} \su

文章目录基本酉变换WALSH-HADAMARD TRANSFORMSsequency-ordered WHTSLANT TRANSFORMHaar TransformGonzalez R. C. and Woods R. E. Digital Image Processing (Forth Edition)基本酉变换一维的变换:t=Af,f=AHt,AH=A∗T,AHA=I.\mathbf{t} = \mathbf{A} \mathbf{f}, \\\mathbf{f} = \mathbf

文章目录基本酉变换othersFourier-related TransformsDFTDHTDCT与DFT的联系DST与DFT的联系Gonzalez R. C. and Woods R. E. Digital Image Processing (Forth Edition)基本酉变换一维的变换:t=Af,f=AHt,AH=A∗T,AHA=I.\mathbf{t} = \mathbf{A} \mathbf{f}, \\\mathbf{f} = \mathbf{A}^{H} \mathbf{

文章目录概定义RGBCMYCMYKHSI相互的转换RGB <=> CMYCMY <=> CMYKCMY > CMYKCMYK > CMYRGB <=> HSIRGB > HSIHSI > RGB代码示例Gonzalez R. C. and Woods R. E. Digital Image Processing (Forth Edition)概除了我们熟悉的RGB模式来表示图片, 还有其他很多种图片表示方式. 其实我现在很想要知道的一点是

文章目录基本滤波的推导特别的情况特别的例子Signals, Systems and Inference, Chapter 11: Wiener Filtering (mit.edu)基本在图像处理的时候, 遇到了这个维纳滤波, 其推导的公式不是很理解, 于是上网查了查, 并做个简单的总结.符号说明x[k]]x[k]]x[k]]观测信号xxx的第k个元素y^\hat{y}y^​为yyy的一个估计vvv噪声信号e[k]e[k]e[k]误差, 为e[k]=

文章目录概主要内容RKHS-wiki概这里对RKHS做一个简单的整理, 之前的理解错得有点离谱了.主要内容首先要说明的是, RKHS也是指一种Hilbert空间, 只是其有特殊的性质.Hilbert空间H\mathcal{H}H, 其中的每个元素f:X→Kf: \mathcal{X} \rightarrow \mathbb{K}f:X→K, 并由内积⟨⋅,⋅,⟩H\langle \cdot, \cdot, \rangle_{\mathcal{H}}⟨⋅,⋅,⟩H​建立联系. 我们考虑如下的

文章目录LaplacianUNSHARP MASKING AND HIGHBOOST FILTERINGFirst-Order DerivativesRoberts cross-gradientSobel operators上一部分介绍的blur能够将图片模糊化, 这部分介绍的是突出图片的边缘的细节.什么是边缘呢? 往往是像素点跳跃特别大的点, 这部分和梯度的概念是类似的, 可以如下定义图片的一阶导数而二阶导数:∂f∂x=f(x+1)−f(x),∂2f∂x2=f(x+1)+f(x−1)−2f(x).

文章目录FILTERSBox Filter KernelsLowpass Gaussian Filter KernelsOrder-Statistic (Nonlinear) FiltersGonzalez R. C. and Woods R. E. Digital Image Processing (Forth Edition).import cv2import matplotlib.pyplot as pltimport numpy as npFILTERSfilters实际上就是通过

文章目录HISTOGRAM EQUALIZATION代码示例HISTOGRAM MATCHING (SPECIFICATION)其它Gonzalez R. C. and Woods R. E. Digital Image Processing (Forth Edition).令rk,k=0,1,2,⋯ ,L−1r_k, k = 0, 1,2, \cdots, L-1rk​,k=0,1,2,⋯,L−1 表示图片密度值为kkk,h(rk)=nk, k=0,1,⋯ ,L−1,h(r_k) = n_k,

文章目录定义性质A(θ)A(\theta)A(θ)极大似然估计最大熵例子Bernoulli指数分布正态分布Choi H. I. Lecture 4: Exponential family of distributions and generalized linear model (GLM).定义定义: 一个分布具有如下形式的密度函数:fθ(x)=1Z(θ)h(x)e⟨T(x),θ⟩,f_{\theta}(x) = \frac{1}{Z(\theta)} h(x) e^{\langle T(x)

文章目录定义充分统计量的判定最小统计量例子U[0,θ]U[0, \theta]U[0,θ]U[α,β]U[\alpha, \beta]U[α,β]PoissonNormal指数分布GammaSufficient statistic - WikipediaSufficient statistic - arizona定义统计量是一些随机样本X1,X2,⋯ ,XnX_1, X_2, \cdots, X_nX1​,X2​,⋯,Xn​的函数T=r(X1,X2,⋯ ,Xn).T = r(X_1, X

文章目录概主要内容最终的目标代码Ng I., Fang Z., Zhu S., Chen Z. and Wang J. Masked Gradient-Based Causal Structure Learning. arXiv preprint arXiv:1911.10500, 2019.概非线性, 自动地学习因果图.主要内容NOTEARS将有向无环图凝练成了易处理的条件, 本文将这种思想扩展至非线性的情况:Xi=fi(Xpa(i))+ϵi,X_i = f_i(X_{\mathrm{p

文章目录概主要内容等价条件的推导tr(I−W)−1=d\mathrm{tr}(I-W)^{-1} = dtr(I−W)−1=dtr(eW)=d\mathrm{tr}(e^W)=dtr(eW)=dtr(eW∘W)=d\mathrm{tr}(e^{W \circ W}) =dtr(eW∘W)=d性质的推导求解代码Zheng X., Aragam B., Ravikumar P. and Xing E. DAGs with NO TEARS: Continuous Optimization for Struc

文章目录概主要内容定义Gumbel-Max trickGumbel trick 用于归一化代码概感觉这个分布的含义很有用啊, 能预测‘最大’, 也就是自然灾害, 太牛了.主要内容定义[Gumbel distribution-wiki](Gumbel distribution - Wikipedia)其分布函数和概率密度函数分别为:F(x;μ,β)=e−e−(x−μ)/β,f(x;μ,β)=1βe−[e−(x−μ)/β+(x−μ)/β]F(x; \mu, \beta) = e^{-e^{-(x

文章目录基本的概念重要的结果X⊥Z∣b(X)X \perp Z | b(X)X⊥Z∣b(X)(r0,r1)⊥Z∣b(X)(r_0, r_1) \perp Z | b(X)(r0​,r1​)⊥Z∣b(X)*若:*(r0,r1)⊥Z∣X,0<P(Z=z∣X)<1,(r_0, r_1) \perp Z | X, \quad 0 < P(Z=z|X) < 1,(r0​,r1​)⊥Z∣X,0<P(Z=z∣X)<1,*且:*P(Z=z∣X=x)=P(Z=z∣X=x′)=p(

文章目录概主要内容一个有趣的应用Prabhushankar M., Kwon G., Temel D. and AlRegib G. Contrastive explanation in neural networks. In 2020 IEEE International Conference on Image Process (ICIP), 2020.Prabhushankar M., AlRegib G. Extracting causal visual features for limit

文章目录概主要内容CAMGrad-CAMGrad-CAM++Score-CAM最后代码Zhou B., Khosla A., Lapedriza A., Oliva A. and Torralba A. Learning Deep Features for Discriminative Localization. CVPR, 2016.Selvaraju R., Das A., Vedantam R>, Cogswell M., Parikh D. and Batra D.Grad-CAM:

文章目录Standardization非参数情况Censoring参数模型Time-varying静态IP weighting无参数Censoring参数模型censoring条件下 VTime-varyingG-estimation非参数模型参数模型Time-varyingPropensity ScoresInstrumental VariablesBinary Linear SettingContinuous Linear SettingNonparametric IdentificationDiffe

文章目录概主要内容CDENDENIETDE, TIE, PDE, PIEJudea Pearl. Direct and indirect effects. In Proceedings of the 17th conference on uncertainty in artificial intelligence. Morgan Kaufmann Publishers Inc., 2001.概CDE: Controlled Direct Effect;NDE: Natural Direct Ef

文章目录22.1 The target trial22.2 Causal effects in randomized trails22.3 Causal effects in observational analyses that emulate a target trial22.4 Time zero22.5 A unified analysis for causal inferenceFine PointGrace periodsTechnical PointControlled direct effe

文章目录21.1 The g-formula for time-varying treatments21.2 IP weighting for time-varying treatments21.3 A doubly robust estimator for time-varying treatments21.4 G-estimation for time-varying treatments21.5 Censoring is a time-varying treatmentFine PointTreatm

文章目录20.1 The elements of treatment-confounder feedback20.2 The bias of traditional methods20.3 Why traditional methods fail20.4 Why traditional methods cannot be fixed20.5 Adjusting for past treatmentFine PointRepresenting feedback cycles with acyclic grap

文章目录19.1 The causal effect of time-varying treatments19.2 Treatment strategies19.3 Sequentially randomized experiments19.4 Sequential exchangeability19.5 Identifiability under some but not all treatment strategies19.6 Time-varying confounding and time-vary

文章目录18.1 The different goals of variable selection18.2 Variables that induce or amplify bias18.3 Causal inference and machine learning18.4 Doubly robust machine learning estimators18.5 Variable selection is a difficult problemFine PointVariable selection p

文章目录17.1 Hazards and risks17.2 From hazards to risks17.3 Why censoring matters17.4 IP weighting of marginal structural models17.5 The parametric g-formula17.6 G-estimation of structural nested modelsFine PointCompeting eventsThe hazards of hazard ratiosMod

文章目录16.1 The three instrumental conditions16.2 The usual IV estimand16.3 A fourth identifying condition: homogeneity16.4 An alternative fourth condition: monotonicity16.5 The three instrumental conditions revisited16.6 Instrumental variable estimation vers

文章目录15.1 Outcome regression15.2 Propensity scores15.3 Propensity stratification and standardization15.4 Propensity matching15.5 Propensity models, structural models, predictive modelsFine PointNuisance parametersEffect modification and the propensity score

文章目录14.1 The causal question revisited14.2 Exchangeability revisited14.3 Structural nested mean models14.4 Rank preservation14.5 G-estimation14.6 Structural nested models with two or more parametersFine PointRelation between marginal structural models and

文章目录13.1 Standardization as an alternative to IP weighting13.2 Estimating the mean outcome via modeling13.3 Standardizing the mean outcome to the confounder distribution13.4 IP weighting or standardization13.5 How seriously do we take our estimates?Fine Po

文章目录12.1 The causal question12.2 Estimating IP weights via modeling12.3 Stabilized IP weights12.4 Marginal structural models12.5 Effect modification and marginal structural models12.6 Censoring and missing dataFine PointSetting a bad exampleChecking positi

文章目录11.1 Data cannot speak for themselves11.2 Parametric estimators of the conditional mean11.3 Nonparametric estimators of the conditional mean11.4 SmoothingThe bias-variance trade-offFine PointFisher consistencyModel dimensionality and the relation betwe

文章目录10.1 Identification versus estimation10.2 Estimation of causal effects10.3 The myth of the super-population10.4 The conditionality "principle"The curse of dimensionalityFine PointHonest confidence intervalsUncertainty from systematic biasTechnical Poin

文章目录9.1 Measurement ErrorThe structure of measurement error9.3 Mismeasured confounders9.4 Intention-to-treat effect: the effect of a misclassified treatment9.5 Per-protocol effectFine PointThe strength and direction of measurement biasPer-protocol analyses