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英翻亞美尼亞語

其他改進1：It has been shown that the original Fisher’s Linear Discriminant criterion can be replaced by the modified Fisher’s Linear Discriminant criterion in the course of solving the discriminant vectors of the optimal set in [18].

方法3.1和3.2 翻譯弱點：Although, the PCA+Null Space method and the variation proposed by Yang et al.翻譯社 use the original sample space 翻譯公司 applying PCA and using all eigenvectors corresponding to the nonzero eigenvalues make these methods impractical for face recognition applications when the training set size is large. This is due to the fact that the computational expense of training becomes very large.

In this paper, a new method is proposed which addresses the limitations of other methods that use the null space of SW to find the optimal projection vectors.

。-> 翻譯社 ,-> 翻譯公司 的-> 翻譯這一類方式會碰著 翻譯問題：However翻譯社 since face images have similar structure, the image vectors are correlated, and any image in the sample space can be represented in a lower-dimensional subspace without losing a significant amount of information.

下面入手下手定義手藝問題：Face recognition can be defined as the identification of individuals from images of their faces by using a stored database of faces labeled with people’s identities.

RECENTLY, due to military翻譯社 commercial 翻譯公司 and law enforcement applications翻譯社 there has been much interest in automatically recognizing faces in still and video images. This research spans several disciplines such as image processing, pattern recognition, computer vision, and neural networks. The data come from a wide variety of sources. One group of sources is the relatively controlled format images such as passports, credit cards 翻譯公司 photo IDs翻譯社 drivers’ licenses翻譯社 and mug shots.

方式的錯誤錯誤：However 翻譯公司 removing the null space of SB by dimensionality reduction will also remove part of the null space of SW and may result in the loss of important discriminative information [13] 翻譯公司 [15]翻譯社 [16]. Furthermore, SB is whitened as a part of this method. This whitening process can be shown to be redundant and 翻譯公司 therefore翻譯社 should be skipped.（講體式格局的毛病錯誤就是為了「轉」到本身的研究 翻譯社）

方式描寫：This method uses the simultaneous diagonalization method [8]. First, the null space of SB is removed and翻譯社 then翻譯社 the projection vectors that minimize the within-class scatter in the transformed space are selected from the range space of SB.

體式格局2的特點/長處：Thus翻譯社 by applying this method 翻譯公司 we find the projection directions that on one hand maximize the Euclidean distance between the face images of different classes and on the other minimize the distance between the face images of the same class. This ratio is maximized when the column vectors of the projection matrix W are the eigenvectors of ....

In Section 2, the Discriminative Common Vector approach is introduced. In Section 3翻譯社 we describe the data sets and experimental results. Finally 翻譯公司 we formulate our conclusions in Section 4.

。-> 翻譯社 ,-> 翻譯公司 的-> 翻譯回頭再「承」：

起：問題描寫，從遠到近交卸你的論文要解問題的範圍。

合：研究方針

一些觀察：In our experiments, we observed that the performance of the Null Space method depends on the dimension of the null space of SW in the sense that larger dimension provides better performance. Thus, any kind of preprocessing that reduces the original sample space should be avoided.

體例2：這個方法與前面 翻譯方式有關，它是為了改進方法1 翻譯錯誤謬誤來的；根基上，如果翻譯公司有兩類的方式，你要交卸這兩類方式分歧的處所在那裡 翻譯社
The Linear Discriminant Analysis (LDA) method is proposed in [6] and [7]. （這裡用此刻式有點不太准確，天成翻譯公司會建議用曩昔式，因為這兩篇論文的提出已疇昔了翻譯

。-> 翻譯社 ,-> 翻譯公司 的-> 翻譯體式格局2約略的描述：This method overcomes the limitations of the Eigenface method by applying the Fisher’s Linear Discriminant criterion. This criterion tries to maximize the ratio（數學式子，省略）where SB is the between-class scatter matrix, and SW is the within-class scatter matrix.

導論要怎麼寫？「起承轉合」這四個字倒可以幫你的論文導論成立一個架構：

本研究 翻譯限制：Thus, the proposed method can be only used when the dimension of the sample space is larger than the rank of SW.

。-> 翻譯社 ,-> 翻譯公司 的-> 翻譯 要寫論文的人就憑據上面起承轉合的四步寫法，找兩到三篇期刊論文來剖析一下，分析一下每篇論文寫法 翻譯「同、異」，然後將之紀錄下來，今後自己 翻譯寫作就會順利 翻譯多。翻譯-> 翻譯社 ,-> 翻譯公司 的-> 翻譯

合：研究目 翻譯（Purpose) 翻譯公司用很明白的文字定義你的研究方針，有時也可以或許再加上對本身體式格局價值的評議 翻譯社

）翻譯-> 翻譯社 ,-> 翻譯公司 的-> 翻譯

再轉：對一篇完全的論文而言，導論是「起」，所以，一般的學位論文或期刊長文導論的最後一段還要再加上後面各章節 翻譯簡要描述。

方式2的問題：In face recognition tasks翻譯社 this method cannot be applied directly since the dimension of the sample space is typically larger than the number of samples in the training set. As a consequence翻譯社 SW is singular in this case. This problem is also known as the “small sample size problem” [8].

解決問題的方式1：The Eigenface method has been proposed for finding such a lowerdimensional subspace [5]. The key idea behind the Eigenface method, which uses Principal Component Analysis (PCA) 翻譯公司 is to find the best set of projection directions in the sample space that will maximize the total scatter across all images such that （數學式子，省略）is maximized. Here, ST is the total scatter matrix of the training set samples 翻譯公司 and W is the matrix whose columns are the orthonormal projection vectors. The projection directions are also called the eigenfaces. Any face image in the sample space can be approximated by a linear combination of the significant eigenfaces. The sum of the eigenvalues that correspond to the eigenfaces not used in reconstruction gives the mean square error of reconstruction.

方式弱點1.1：This method is an unsupervised technique since it does not consider the classes within the training set data. In choosing a criterion that maximizes the total scatter, this approach tends to model unwanted within-class variations such as those resulting from the differences in lighting, facial expression 翻譯公司 and other factors [6] 翻譯公司 [7].

。-> 翻譯社 ,-> 翻譯公司 的-> 翻譯（後註：這一篇我清理了兩個多小時喔翻譯你可以將相幹研究分成兩或三大類（有需要的話，大類還可以，再分一級），然後每大類約略的依年代介紹相幹研究 翻譯方式和它們可能 翻譯瑕玷 翻譯社

本想再解析另外一篇論文的導論，但篇幅有點太長了，就此打住翻譯

）

方式2的相關研究論文四篇：In the last decade numerous methods have been proposed to solve this problem 翻譯公司 Tian et al. [9] used the Pseudoinverse method by replacing ... with its pseudoinverse. The Perturbation method is used in [2] and [10]翻譯社 where a small perturbation matrix  is added to SW in order to make it nonsingular. Cheng et al. [11] proposed the Rank Decomposition method based on successive eigendecompositions of the total scatter matrix ST and the between-class scatter matrix SB.

。-> 翻譯社 ,-> 翻譯公司 的-> 翻譯承：相幹研究，具體的聲名這個問題的領域有兩些相關的研究翻譯

It is a difficult problem as there are numerous factors such as 3D pose翻譯社 facial expression翻譯社 hair style 翻譯公司 make up, etc., which affect the appearance of an individual’s facial features. In addition to these varying factors 翻譯公司 lighting 翻譯公司 background, and scale changes make this task even more challenging. Additional problematic conditions include noise, occlusion, and many other possible factors.

相幹研究的缺點：However翻譯社 the above methods are typically computationally expensive since the scatter matrices are very large (e.g., images of size 256 by 256 yield scatter matrices of size 65 翻譯公司536 by 65,536). Swets and Weng [7] proposed a two stage PCA+LDA method 翻譯公司 also known as the Fisherface method 翻譯公司 in which PCA is first used for dimension reduction so as to make SW nonsingular before the application of LDA.

）
。-> 翻譯社 翻譯社-> 翻譯公司 的-> 翻譯

。-> 翻譯社 ,-> 翻譯公司 的-> 翻譯一篇學術論文除摘要給人 翻譯第一個感受很首要外，第一章的導論部分可能也是決意翻譯公司這篇論文會不會被接收的關鍵，很多人一樣的要把導論留到最後寫，我的建議是一路頭就要寫，寫完就交給指點傳授改，因為在導論中，問題的定義已出來，對問題的約略走向也已約略的講清楚 翻譯社大部分寫科技論文的學生對體例的描寫、嘗試 翻譯進行、資料 翻譯剖析等可能較量沒有問題，但要整理出一篇學術論文可能會有障礙，這部分要和指導教授多溝通幾回翻譯

體例3.1：Another novel method, the PCA+Null Space method, was proposed by Huang et al. in [15] for dealing with the small sample size problem.

承：相幹研究─
Many methods have been proposed for face recognition within the last two decades [1] 翻譯公司 [3]. （提出什麼體例都用現在完成式來表達）

。-> 翻譯社 ,-> 翻譯公司 的-> 翻譯體例4：Last翻譯社 the Direct-LDA method is proposed in [12].

。-> 翻譯社 翻譯社-> 翻譯公司 的-> 翻譯針對上面弱點 翻譯改良：However, in order to make SW nonsingular, some directions corresponding to the small eigenvalues of ST are thrown away in the PCA step. Thus, applying PCA for dimensionality reduction has the potential to remove dimensions that contain discriminative information [12], [13] 翻譯公司 [14]翻譯社 [15], [16]. Chen et al. [17] proposed the Null Space method based on the modified Fisher’s Linear Discriminant criterion（數學式子，省略）This method has been proposed to be used when the dimension of the sample space is larger than the rank of the within-class scatter matrix SW.

作法：In this method, all image samples are first projected onto the null space of SW 翻譯公司 resulting in a new within-class scatter that is a zero matrix. Then, PCA is applied to the projected samples to obtain the optimal projection vectors.

轉：研究 翻譯需要性，既然有了一些相關研究，那為什麼你還要做這個研究。

其他改進2：Chen et al. also proved that by applying this method 翻譯公司 the modified Fisher’s Linear Discriminant criterion attains its maximum.

再轉：

臉部辨識為什麼很堅苦，它們遭到哪些身分的影響：This task is complex and can be decomposed into the smaller steps of detection of faces in a cluttered background, localization of these faces followed by extraction of features from the face regions 翻譯公司 and, finally, recognition and verification [2].

。-> 翻譯社 ,-> 翻譯公司 的-> 翻譯相關體例出來了：Among these methods翻譯社 appearance-based approaches operate directly on images or appearances of face objects, and process the images as two-dimensional holistic patterns. In these approaches翻譯社 a two-dimensional image of size w by h pixels is represented by a vector in a wh-dimensional space. Therefore, each facial image corresponds to a point in this space. This space is called the sample space or the image space, and its dimension typically is very high [4]. 注意：對這些方式的描寫掃數用現在式，這是因為這些方式此刻進行也是這樣（事實）。。-> 翻譯社 ,-> 翻譯公司 的-> 翻譯

。-> 翻譯社 ,-> 翻譯公司 的-> 翻譯

方式描寫：In this method, at first, PCA is applied to remove the null space of ST , which contains the intersection of the null spaces of SB and SW. Then 翻譯公司 the optimal projection vectors are found in the remaining lowerdimensional space by using the Null Space method. The difference between the Fisherface method and the PCA+Null Space method is that for the latter 翻譯公司 the within-class scatter matrix in the reduced space is typically singular. This occurs because all eigenvectors corresponding to the nonzero eigenvalues of ST are used for dimension reduction.

-> 翻譯社 ,-> 翻譯公司 的-> 翻譯

However, they did not propose an efficient algorithm for applying this method in the original sample space. Instead, a pixel grouping method is applied to extract geometric features and reduce the dimension of the sample space. Then, they applied the Null Space method in this new reduced space.

有關翻譯的問題迎接諮詢天成翻譯社

翻譯-> 翻譯社 ,-> 翻譯公司 的-> 翻譯轉：研究 翻譯需要性

起：問題描述

體例毛病錯誤1.2：Additionally翻譯社 since the criterion does not attempt to minimize the withinclass variation, the resulting classes may tend to have more overlap than other approaches. Thus翻譯社 the projection vectors chosen for optimal reconstruction may obscure the existence of the separate classes.

公正翻譯推薦

下面我就用一篇2006年揭橥在IEEE trans. on Pattern Analysis and Machine Intelligence上面 翻譯一篇文章Discriminative Common Vectors for Face Recognition來跟巨匠做申明，因為這篇講「臉部辨識」 翻譯文章是長文，導論的部門有點長：

The remainder of the paper is organized as follows: （這一句話是科技陳腔濫調，照著寫就對了；也請注重標點符號。。-> 翻譯社 翻譯社-> 翻譯公司 的-> 翻譯

這篇文章的導論一最早講行使，上面的闡述對照一般化，後面的闡述將規模縮小：A more challenging class of application imagery includes real-time detection and recognition of faces in surveillance video images 翻譯公司 which present additional constraints in terms of speed and processing requirements [1].

體式格局3.2：Yang et al. applied a variation of this method in [16]. After dimension reduction 翻譯公司 they split the new within-class scatter matrix, ... (where PPCA is the matrix whose columns are the orthonormal eigenvectors corresponding to the nonzero eigenvalues of ST )翻譯社 into its null space .... Then 翻譯公司 all the projection vectors that maximize the betweenclass scatter in the null space are chosen. If, according to some criterion 翻譯公司 more projection vectors are needed 翻譯公司 the remaining projection vectors are obtained from the range space.