外文翻譯--基于局部二值模式多分辨率的灰度和旋轉(zhuǎn)不變性的紋理分類（節(jié)選）

1、<p>　　2700單詞，4460漢字</p><p>　　出處：Ojala T, Pietikäinen M, Mäenpää T. Multiresolution Gray-Scale and Rotation Invariant Texture Classification with Local Binary Patterns[J]. IEEE Transa

2、ctions on Pattern Analysis & Machine Intelligence, 2002, 24(7):971-987.</p><p>　　本科生畢業(yè)設(shè)計(jì)（論文）</p><p><b>　　外文翻譯及原文</b></p><p>　　題 目：Multiresolution Gray-Scale and Rot

3、ation</p><p>　　Invariant Texture Classification with </p><p>　　Local Binary Patterns（section 2） </p><p>　　姓 名： </p><p>　　學(xué) 號：

4、 </p><p>　　學(xué) 院： 數(shù)學(xué)與計(jì)算機(jī)科學(xué)學(xué)院 </p><p>　　專 業(yè)： 信息與計(jì)算科學(xué)專業(yè) </p><p>　　年 級： </p><p>　　指導(dǎo)教師：

5、 （簽名）</p><p>　　系主任（或教研室主任）： （簽章）</p><p>　　基于局部二值模式多分辨率的灰度</p><p>　　和旋轉(zhuǎn)不變性的紋理分類（節(jié)選）</p><p>　　Timo Ojala, Matti Pietikaè inen, Senior Member, IEEE, an

6、d Topi Maèenpaèaè</p><p><b>　　摘要：</b></p><p>　　本文描述了理論上非常簡單但非常有效的，基于局部二值模式的、樣圖的非參數(shù)識別和原型分類的，多分辨率的灰度和旋轉(zhuǎn)不變性的紋理分類方法。此方法是基于結(jié)合某種均衡局部二值模式，是局部圖像紋理的基本特性，并且已經(jīng)證明生成的直方圖是非常有效的紋理特征。

7、我們獲得一個一般灰度和旋轉(zhuǎn)不變的算子，可表達(dá)檢測有角空間和空間結(jié)構(gòu)的任意量子化的均衡模式，并提出了結(jié)合多種算子的多分辨率分析方法。根據(jù)定義，該算子在圖像灰度發(fā)生單一變化時具有不變性，所以所提出的方法在灰度發(fā)生變化時是非常強(qiáng)健的。另一個優(yōu)點(diǎn)是計(jì)算簡單，算子在小鄰域內(nèi)或同一查找表內(nèi)只要幾個操作就可實(shí)現(xiàn)。在旋轉(zhuǎn)不變性的實(shí)際問題中得到了良好的實(shí)驗(yàn)結(jié)果,與來自其他的旋轉(zhuǎn)角度的樣品一起以一個特別的旋轉(zhuǎn)角度試驗(yàn)而且測試得到分類, 證明了基于簡單旋轉(zhuǎn)的

8、發(fā)生統(tǒng)計(jì)學(xué)的不變性二值模式的分辨是可以達(dá)成。這些算子表示局部圖像紋理的空間結(jié)構(gòu)的又一特色是，由結(jié)合所表示的局部圖像紋理的差別的旋轉(zhuǎn)不變量不一致方法，其性能可得到進(jìn)一步的改良。這些直角的措施共同證明了這是旋轉(zhuǎn)不變性紋理分析的非常有力的工具。</p><p>　　關(guān)鍵詞：非參數(shù)的，紋理分析，Outex，Brodatz，分類，直方圖，對比度</p><p>　　2 灰度和旋轉(zhuǎn)不變性的局部二值模式

9、</p><p>　　我們通過定義單色紋理圖像的一個局部鄰域的紋理T，如 P（P>1）個象素點(diǎn)的灰度級聯(lián)合分布，來描述灰度和旋轉(zhuǎn)不變性算子：</p><p><b>　?。?）</b></p><p>　　其中，gc為局部鄰域中心像素點(diǎn)的灰度值，gp（p=0，1…P-1）為半徑R(R>0)的圓形鄰域內(nèi)對稱的空間象素點(diǎn)集的灰度值。&l

10、t;/p><p><b>　　圖1</b></p><p>　　如果gc的坐標(biāo)是（0,0），那么gp的坐標(biāo)為。圖1舉例說明了圓形對稱鄰域集內(nèi)各種不同的（P,R）。不完全落在中心點(diǎn)鄰域內(nèi)的像素點(diǎn)的灰度值采用插值法估計(jì)。</p><p>　　2.1 灰度不變性的達(dá)成</p><p>　　作為灰度不變性的第一步，在不丟失任何圖像信

11、息的前提下，我們從圓形對稱鄰域集gp（p=0,……P-1）中減去中心點(diǎn)（gc）的灰度值，即令：</p><p><b>　　（2）</b></p><p>　　然后，我們假設(shè)差分獨(dú)立于，這樣我們就可以把式（2）式分解為：</p><p><b>　　（3）</b></p><p>　　實(shí)際上，嚴(yán)格的

12、獨(dú)立性是無法達(dá)成的，因此，被分解的因式只是聯(lián)合分布的一個近似值。然而，當(dāng)我們在旋轉(zhuǎn)中可以保持灰度不變性的話，我們愿意承擔(dān)丟失一些圖像小信息的可能。也就是說，因式在（3）中描述了圖像的全局亮度，但并不為紋理分析提供有用信息。因此，原始的聯(lián)合灰度級因式（1）的許多紋理特征信息可由聯(lián)合差分因式表達(dá)[1]：</p><p><b>　?。?）</b></p><p>　　這是

13、一個有高度識別能力的紋理算子，可以算出P空間中各種模式下每個像素點(diǎn)鄰域的直方圖。對于固定的區(qū)域，在各個方向的差別為零。在一個慢慢傾斜的邊緣，該算子可算出沿傾斜方向差分最大的點(diǎn)和差分為零的點(diǎn)，對于斑點(diǎn)而言，各個方向的差分都是很大的。</p><p>　　有正負(fù)之分的差分不受平均亮度改變的影響，因此，聯(lián)合差分因式對于灰度變化具有不變性。我們所得到的關(guān)于灰度計(jì)數(shù)不變性只考慮差分符號而非它們的精確值：</p>

14、<p><b>　　(5)</b></p><p><b>　　其中，</b></p><p><b>　　(6)</b></p><p>　　通過為每一個的符號賦一個二項(xiàng)式因子，我們把式（5）轉(zhuǎn)換為一個獨(dú)特的碼來刻畫局部圖像紋理的空間結(jié)構(gòu)的特性：</p><p>

15、;<b>　　(7)</b></p><p>　　Local Binary Patterns這個名字反映了LBP算子的泛函性，即第一個局部鄰域點(diǎn)的灰度值是中心像素點(diǎn)進(jìn)入二值模式的開始。算子是通過對灰度的任何單調(diào)變化定義不變量，也就是，只要保持圖像灰度值的順序不變，算子所產(chǎn)生的LBP碼就不變。</p><p>　　如果我們設(shè)置（P=8,R=1），我們得到這與我們在文獻(xiàn)[

16、2]中提到的LBP是類似的。和LBP之間有兩個不同點(diǎn)：1)鄰域集內(nèi)的像素點(diǎn)被編入索引以形成一個循環(huán)鏈，2)對角線上像素點(diǎn)的灰度值由插值法確定。兩者的修改都必需獲得圓形對稱鄰域集，這考慮到源自的旋轉(zhuǎn)不變式之一。</p><p>　　2.2旋轉(zhuǎn)不變性的達(dá)成</p><p>　　由鄰域集中P個像素點(diǎn)對應(yīng)個不同的二值模式，算子會生成個不同的輸出值。當(dāng)圖像被旋轉(zhuǎn)時，的灰度值會對應(yīng)地繞著的四周沿著圓周

17、的邊界移動。始終被指定為元素(0,R)的灰度值，而恰恰旋轉(zhuǎn)一個特定的二值模式后自然生成一個不同的值。這不適用于只由0s（或1s）組成的旋轉(zhuǎn)任何角度始終保持不變的模式。為了要消除旋轉(zhuǎn)的影響，也就是，要分配一個獨(dú)特的標(biāo)識符給每個旋轉(zhuǎn)不變性的局部二值模式，我們定義：</p><p><b>　　(8)</b></p><p>　　其中ROR(x,i) 執(zhí)行一個循環(huán)的位方法的

18、P-位元x i次的變換。就圖像像素點(diǎn)而言，式(8)只簡單對應(yīng)于被多次順時針方向旋轉(zhuǎn)的鄰域集，因而最有效位元的一個最大碼從啟動,為0。</p><p>　　量化了對特定的微特征的個別旋轉(zhuǎn)不變性模式的發(fā)生統(tǒng)計(jì)學(xué)；因此該模式可作為特征檢測器。圖2舉例說明了當(dāng)P=8時的36種獨(dú)特的旋轉(zhuǎn)不變二值模式，也就是說，可以有36個不同的值。比如說，圖案#0檢測到明亮的斑點(diǎn)，#8有暗點(diǎn)和平坦的區(qū)域，#4有邊緣。如果我們設(shè)定 R=1，

19、符合灰度和旋轉(zhuǎn)不變性算子正如我們在[3]中指定了的 LBPROT。</p><p><b>　　圖 2</b></p><p>　　2.3基于均衡模式改進(jìn)的旋轉(zhuǎn)不變性和有角空間的更佳量化</p><p>　　然而，我們的實(shí)際經(jīng)驗(yàn)已經(jīng)顯示LBPROT 同樣不能提供非常好的識別，這點(diǎn)我們也總結(jié)在[3]。這有兩個原因：1)LBPROT中36種互相獨(dú)立

20、的模式聯(lián)合體的發(fā)生頻率變化非常大，2)有角空間45°間隔的粗糙量化。</p><p>　　我們已經(jīng)觀測得知，特定的LBP可描述絕大多數(shù)的基本紋理特征，有時可描述超過90%的3×3模式里所有的紋理。這將和實(shí)驗(yàn)中用到的圖像數(shù)據(jù)統(tǒng)計(jì)學(xué)一起在第3節(jié)中加以詳細(xì)闡述。當(dāng)它們具有一個共同點(diǎn)時，我們稱這種基本模式為“均衡模式”，即包含少許空間變換的均衡圓形循環(huán)結(jié)構(gòu)。均衡模式的例子如圖2的第一行，它們就像模板一

21、樣作用于各種微結(jié)構(gòu)，諸如明亮的斑點(diǎn)(0)，平滑區(qū)域或者暗色斑點(diǎn)(8)，以及按曲率正負(fù)變化的邊緣(1-7)等等。</p><p>　　為了要正式定義“均衡”模式，我們引入U(xiǎn)值（“模式”），“均衡”模式與U“模式”下的空間變換碼（0/1的跳躍）對應(yīng)。例如，模式和的U值為0，而圖2第一列中的其它七種模式的U值為2，即這些模式中最多只有2次0/1的跳躍。類似的，其它27種模式的U值至少為4。我們指定U值不大于2的為“均衡

22、”模式，并提出了替代的基于灰度和旋轉(zhuǎn)不變紋理的算子如下：</p><p><b>　　(9)</b></p><p><b>　　其中</b></p><p><b>　　(10)</b></p><p>　　標(biāo)在右上角的riu2反映了旋轉(zhuǎn)不變“均衡”模式的用處——U值最大為2

23、。根據(jù)定義，P+1“均衡”二值模式可用于P個像素點(diǎn)的圓形對稱鄰域集。方程式(9)指定了一個獨(dú)特的標(biāo)識給這些像素點(diǎn)對應(yīng)模式（）中的二進(jìn)制碼“1”。圖2通過圖案把“均衡”模式表示出來了。在實(shí)踐中，從到的映射有P+2個不同的輸出值，是基于個元素的查找表的最佳實(shí)現(xiàn)。</p><p>　　紋理分析中最終使用的紋理特征是算子作用在紋理樣本之上所得值（即模式標(biāo)識）的累計(jì)直方圖。相對于全獨(dú)立模式的直方圖，“均衡”模式的直方圖之所

24、以能提供更好的識別力，歸結(jié)為它們的統(tǒng)計(jì)特性的差別。全模式累計(jì)直方圖中的“非均衡”模式的相關(guān)比例很小，因而它們的概率得不到可靠的估計(jì)。對樣本和模型直方圖的相異點(diǎn)分析中的有噪估計(jì)會使效果變差。</p><p>　　我們很早就注意到，LBPROT（）的旋轉(zhuǎn)不變性受鄰域集內(nèi)8個像素點(diǎn)所提供的有角空間45°角粗量化的制約。因?yàn)橛薪强臻g的量化被定義為(360°/P)，所以要使用一個更大的P來直接定位。但是

25、，P的選擇還必須考慮一些特定的事項(xiàng)。首先，P和R在某種程度上與給定的R對應(yīng)的圓形鄰域包含的有限的像素點(diǎn)數(shù)（例如，9對于R=1），這里引進(jìn)鄰域的非多余取樣點(diǎn)的數(shù)目上限。其次，包含有個元素的查找表的有效執(zhí)行，要求為P設(shè)定一個實(shí)用的上限。本文中，我們探索P值最大為24，這需要一個能由計(jì)算機(jī)簡單處理16MB的查詢表。</p><p>　　2.4 局部圖像紋理對比度的旋轉(zhuǎn)不變量方差的量度</p><p&

26、gt;　　算子是一個灰度不變性方法，也就是，它的輸出值不受任何灰度轉(zhuǎn)化的影響。它是空間模式的優(yōu)良方法，但根據(jù)定義，丟失了對比度。如果灰度不變性不是必需的，而我們又想要合并局部圖像紋理的對比度，則可用旋轉(zhuǎn)不變量來衡量局部方差：</p><p><b>　　(11)</b></p><p>　　是根據(jù)灰度變化不變量定義的，和是互相補(bǔ)充的，它們的聯(lián)合分布/的數(shù)學(xué)期望是局部圖

27、像紋理旋轉(zhuǎn)不變量強(qiáng)有力的衡量。鑒于此，即使我們在本研究中限制我們自己用到具有相同(P,R)值的和算子，也不會影響我們使用作用于不同鄰域的算子的聯(lián)合分布。</p><p>　　2.5 非參數(shù)的分類法則</p><p>　　在分類階段，我們求出樣本和模型直方圖的相異值作為擬合度測試，這個值由非參數(shù)的統(tǒng)計(jì)檢驗(yàn)來衡量。通過非參數(shù)檢驗(yàn)，關(guān)于紋理分類的假設(shè)，我們可以避免任何可能的錯誤。有許多眾所周知的

28、擬合度統(tǒng)計(jì)量，諸如統(tǒng)計(jì)量和G（對數(shù)似然比）統(tǒng)計(jì)量 [4]。本研究中，測試樣本S被指派給M模型類，它的極大對數(shù)似然統(tǒng)計(jì)量為：</p><p><b>　　(12)</b></p><p>　　其中，B為bin的數(shù)量，和分別對應(yīng)樣本和模型的直方圖維值（bin）為b的概率。方程式（12）是G（對數(shù)似然比）統(tǒng)計(jì)量的直接簡化：</p><p><b

29、>　　(13)</b></p><p>　　其中，表達(dá)式右邊的第一項(xiàng)可以忽略地看作是給定的常數(shù)S。</p><p>　　L是一個非參數(shù)假設(shè)，用于衡量樣本S的似然度，是來自紋理類別還是基于預(yù)分類紋理模型M的準(zhǔn)確概率。在聯(lián)合分布/(12)的情況下，可以直接方式徹底掃描二維直方圖。</p><p>　　樣本和模型分布藉由通過選擇好的算子和掃描紋理樣本和原

30、型，把算子輸出的分類分解成帶有固定維數(shù)的直方圖。因?yàn)橛幸粋€離散輸出值(0→P+1)的固定集，不需要量化，但算子的輸出值直接被累計(jì)成P+2 維的直方圖。每維都能有效提供一個在紋理樣本或原型中遇到的對應(yīng)模式的概率的估計(jì)量。因?yàn)橹挥幸粋€模式小子集可以幾乎包含一個給定的模式，所以毗連的鄰域之間的空間依存關(guān)系是固有地存在于直方圖中的。</p><p>　　方差量度有一個連續(xù)值的輸出，因此，需要特征空間的量化。這可通過在總分

31、類中為每個單獨(dú)的模型圖像都添加一個特征分類來完成，每個特征分類又被分成有相同條目數(shù)的B維。因此，直方圖的維數(shù)的刪除數(shù)值對應(yīng)組合數(shù)據(jù)的百分位（100/B）。從總分布中獲得刪減值并鎖定每維具有相同量的組合數(shù)據(jù)，以保證最高分辨率的量化用于條目數(shù)最大的地方，反之亦然。由于一個低維的直方圖不能提供足夠的分類識別信息，在特征空間量化中所用到的維數(shù)在某種程度上是很重要的。另一方面，因?yàn)榉诸悧l目數(shù)有限，維數(shù)太大可能導(dǎo)致稀疏且不穩(wěn)定的直方圖。根據(jù)經(jīng)驗(yàn)方法

32、，統(tǒng)計(jì)學(xué)文獻(xiàn)時常建議平均每維 10個條目應(yīng)該是足夠的。在實(shí)驗(yàn)方面，我們設(shè)定 B 的數(shù)值，以便這一個條件得到滿足。</p><p>　　2.6 多分辨率分析 </p><p>　　我們已經(jīng)描述了一般旋轉(zhuǎn)不變算子作用于P像素點(diǎn)以R為半徑的圓形對稱鄰域集內(nèi)的像素點(diǎn)，來刻畫局部圖像紋理的空間模式和對比度。通過改變P和R，我們可以了解算子在有角空間的量化和任意空間解析度的作用。多分辨率分析可通

33、過不斷變化的（P,R）的多重算子所提供的聯(lián)合信息來完成。</p><p>　　本研究中，我們通過定義來直接實(shí)現(xiàn)多分辨率分析，聚合相異度相當(dāng)于對應(yīng)LN算子的對數(shù)似然和。LN算子定義如下：</p><p><b>　　(14)</b></p><p>　　其中，N為算子數(shù)，和分別用算子n（n=1，…，N）提取的對應(yīng)樣本和模型直方圖。這個表達(dá)式是基于

34、G統(tǒng)計(jì)量(13)的特性的疊加，即，幾個G檢驗(yàn)結(jié)果可以歸納出一個有深遠(yuǎn)意義的結(jié)果。如果X和Y是獨(dú)立隨機(jī)事件，且，，和分別為S和M的邊緣分布，則</p><p><b>　　[5]</b></p><p>　　通常，不同紋理特征之間的獨(dú)立性假設(shè)是站不住腳的。然而，由于統(tǒng)計(jì)學(xué)的偏差以及高維直方圖的計(jì)算復(fù)雜度，精確的聯(lián)合概率估計(jì)是不可行的。例如， ，和的疊加直方圖包含4680

35、（10×18×26）個單元。為了滿足統(tǒng)計(jì)可靠性的第一法則，即，平均每單元至少要有10個條目，圖像大小至少為（216+2R）(216+2R)個像素。因此，高維直方圖只有當(dāng)真實(shí)圖像大的時候才可靠，這使之變的不切實(shí)際。大的多維直方圖的計(jì)算在計(jì)算速度和內(nèi)存消耗上也是很可觀的。</p><p>　　最近，我們在紋理分割中也成功使用了這種方法，為多分辨率分析中獨(dú)立直方圖的合并做了大量不同選項(xiàng)的比較[6]。

36、本研究中，我們限制至多三個算子的合并。</p><p>　　Multiresolution Gray-Scale and Rotation Invariant Texture Classification with Local Binary Patterns</p><p>　?。╯ection 2）</p><p>　　Timo Ojala, Matti Piet

37、ikaÈ inen, Senior Member, IEEE, and Topi MaÈenpaÈaÈ</p><p><b>　　Abstract：</b></p><p>　　This paper presents a theoretically very simple, yet efficient, multiresolu

38、tion approach to gray-scale and rotation invariant texture classification based on local binary patterns and nonparametric discrimination of sample and prototype distributions. The method is based on recognizing that cer

39、tain local binary patterns, termed “uniform”, are fundamental properties of local image texture and their occurrence histogram is proven to be a very powerful texture feature. We derive a generalized gray-</p><

40、;p>　　Index Terms：Nonparametric, texture analysis, Outex, </p><p>　　Brodatz, distribution, histogram, contrast.</p><p>　　2 GRAY SCALE AND ROTATION INVARIANT LOCAL BINARY PATTERNS</p>&l

41、t;p>　　We start the derivation of our gray scale and rotation invariant texture operator by defining texture T in a local neighborhood of a onochrome texture image as the joint distribution of the </p><p>

42、　　gray levels of P (P > 1) image pixels:</p><p><b>　　（1）</b></p><p>　　where gray value gc corresponds to the gray value of the center pixel of the local neighborhood and （p=0，1…P-

43、1） correspond to the gray values of P equally spaced pixels on a circle of radius R (R > 0) that form a circularly symmetric neighbor set.</p><p>　　If the coordinates of are (0,0), then the coordinates of

44、 are given by Fig.1 illustrates circularly symmetric neighbor sets for various (P,R). The gray values of neighbors which do not fall exactly in the center of pixels are estimated by interpolation.</p><p>　

45、　2.1 Achieving Gray-Scale Invariance</p><p>　　As the first step toward gray-scale invariance, we subtract,without losing information, the gray value of the center pixel () from the gray values of the circula

46、rly symmetric neighborhood （p=0,……P-1）, giving:</p><p><b>　　（2）</b></p><p>　　Next, we assume that differences are independent of , which allows us to factorize (2):</p><p&

47、gt;<b>　?。?）</b></p><p>　　In practice, an exact independence is not warranted;hence, the factorized distribution is only an approximation of the joint distribution. However, we are willing to acce

48、pt the possible small loss in information as it allows us to achieve invariance with respect to shifts in gray scale.Namely, the distribution in (3) describes the overall luminance of the image, which is unrelated to loc

49、al image texture and, consequently, does not provide useful information for texture analysis. Hence, much of t</p><p><b>　?。?）</b></p><p>　　This is a highly discriminative texture op

50、erator. It records the occurrences of various patterns in the neighborhood of each pixel in a P-dimensional histogram. For constant regions, the differences are zero in all directions. On a slowly sloped edge, the operat

51、or records the highest difference in the gradient direction and zero values along the edge and, for a spot, the differences are high in all directions.</p><p>　　Signed differences gp-gc are not affected by c

52、hanges in mean luminance; hence, the joint difference distribution is invariant against gray-scale shifts. We achieve invariance with respect to the scaling of the gray scale by considering just the signs of the differen

53、ces instead of their exact values:</p><p><b>　　(5)</b></p><p><b>　　where</b></p><p><b>　　(6)</b></p><p>　　By assigning a binomial fa

54、ctor for each sign, we transform (5) into a unique number that characterizes the spatial structure of the local image texture:</p><p><b>　　(7)</b></p><p>　　The name aLocal Binary P

55、atterno reflects the functionality of the operator, i.e., a local neighborhood is thresholded at the gray value of the center pixel into a binary pattern. operator is by definition invariant against any monotonic transf

56、ormation of the gray scale,i.e., as long as the order of the gray values in the image stays the same, the output of the operator remains constant.</p><p>　　If we set (P=8;R=1), we obtain , which is similar

57、to the LBP operator we proposed in [2]. The two differences between and are: 1) The pixels in the neighbor set are indexed so that they form a circular chain and 2) the gray values of the diagonal pixels are determined

58、 by interpolation. Both modifications are necessary to obtain the circularly symmetric neighbor set, which allows for deriving a rotation invariant version of .</p><p>　　2.2 Achieving Rotation Invariance<

59、/p><p>　　The operator produces different output values, corresponding to the different binary patterns that can be formed by the P pixels in the neighbor set. When the image is rotated, the gray values will

60、 correspondingly move along the perimeter of the circle around .Since is always assigned to be the gray value of element (0;R) to the right of rotating a particular binary pattern naturally results in a different valu

61、e. This does not apply to patterns comprising of only 0s (or 1s) which remain c</p><p><b>　　(8)</b></p><p>　　where ROR（x; i） performs a circular bit-wise right shift on the P-bit num

62、ber x i times. In terms of image pixels,（8） simply corresponds to rotating the neighbor set clockwise so many times that a maximal number of the most significant bits, starting from , is 0.</p><p>　　quantifi

63、es the occurrence statistics of individual rotation invariant patterns corresponding to certain microfeatures in the image; hence, the patterns can be considered as feature detectors. Fig. 2 illustrates the 36 unique rot

64、ation invariant local binary patterns that can occur in the case of P=8, i.e., can have 36 different values. For example, pattern #0 detects bright spots, #8 dark spots and flat areas, and #4 edges. If we set R=1, corres

65、ponds to the gray-scale and rotation invariant opera</p><p>　　2.3 Improved Rotation Invariance with “Uniform” Patterns and Finer Quantization of the Angular Space</p><p>　　Our practical experie

66、nce, however, has shown that LBPROT as such does not provide very good discrimination, as we also concluded in [3]. There are two reasons: The occurrence frequencies of the 36 individual patterns incorporated in LBPROT v

67、ary greatly and the crude quantization of the angular space at 45° intervals.</p><p>　　We have observed that certain local binary patterns are fundamental properties of texture, providing the vast major

68、ity, sometimes over 90 percent, of all 3×3 patterns present in the observed textures. This is demonstrated in more detail in Section 3 with statistics of the image data used in the experiments. We call these fundame

69、ntal patterns “uniform” as they have one thing in common, namely, uniform circular structure that contains very few spatial transitions. “Uniform” patterns are illustrate</p><p><b>　　(9)</b></

70、p><p><b>　　where</b></p><p><b>　　(10)</b></p><p>　　Superscript riu2 reflects the use of rotation invariant "uniform" patterns that have U value of at

71、most 2. By definition, exactly P+1 "uniform" binary patterns can occur in a circularly symmetric neighbor set of P pixels.Equation (9) assigns a unique label to each of them corresponding to the number of a1o

72、bits in the pattern (), while the "nonuniform" patterns are grouped under the "miscellaneous" label (P+1). In Fig. 2, the labels of the "uniform" patterns are denoted inside the patterns. In

73、 </p><p>　　The final texture feature employed in texture analysis is the histogram of the operator outputs (i.e., pattern labels) accumulated over a texture sample. The reason why the histogram of "unif

74、orm" patterns provides better discrimination in comparison to the histogram of all individual patterns comes down to differences in their statistical properties. The relative proportion of "nonuniform" pat

75、terns of all patterns accumulated into a histogram is so small that their probabilities cannot be estima</p><p>　　We noted earlier that the rotation invariance of LBPROT() is hampered by the crude 45 quantiz

76、ation of the angular space provided by the neighbor set of eight pixels. A straightforward fix is to use a larger P since the quantization of the angular space is defined by (360°/P).However, certain considerations

77、have to be taken into account in the selection of P. First, P and R are related in the sense that the circular neighborhood corresponding to a given R contains a limited number of pixels (e.g.</p><p>　　2.4 R

78、otation Invariant Variance Measures of the Contrast of Local Image Texture</p><p>　　The operator is a gray-scale invariant measure, i.e.,its output is not affected by any monotonic ransformation of the gray

79、 scale. It is an excellent measure of the spatial pattern, but it, by definition, discards contrast. If gray-scale invariance is not required and we wanted to incorporate the contrast of local image texture as well, we c

80、an measure it with a rotation invariant measure of local variance:</p><p><b>　　(11)</b></p><p>　　is by definition invariant against shifts in gray scale. Since and are complementary,

81、 their joint distribution /is expected to be a very powerful rotation invariant measure of local image texture. Note that, even though we in this study restrict ourselves to using only joint distributions of and operat

82、ors that have the same (P;R) values, nothing would prevent us from using joint distributions of operators computed at different neighborhoods.</p><p>　　2.5 Nonparametric Classification Principle</p>&

83、lt;p>　　In the classification phase, we evaluate the dissimilarity of sample and model histograms as a test of goodness-of-fit, which is measured with a nonparametric statistical test. By using a nonparametric test, we

84、 avoid making any, possibly erroneous, assumptions about the feature distributions. There are many well-known goodness-of-fit statistics such as the chi-square statistic and the G (log-likelihood ratio) statistic [4].In

85、this study, a test sample S was assigned to the class of the model M t</p><p><b>　　(12)</b></p><p>　　where B is the number of bins and and correspond to the sample and model proba

86、bilities at bin b, respectively. Equation (12) is a straightforward simplification of the G(log-likelihood ratio) statistic:</p><p><b>　　(13)</b></p><p>　　where the first term of the

87、 righthand expression can be ignored as a constant for a given S.</p><p>　　L is a nonparametric pseudometric that measures likelihoods that sample S is from alternative texture classes,based on exact probabi

88、lities of feature values of preclassified texture models M. In the case of the joint distribution/ (12) was extended in a straightforward manner to scan through the two-dimensional histograms.</p><p>　　Sampl

89、e and model distributions were obtained by scanning the texture samples and prototypes with the chosen operator and dividing the distributions of operator outputs into histograms having a fixed number of B bins. Since ha

90、s a fixed set of discrete output values (0→P+1), no quantization is required, but the operator outputs are directly accumulated into a histogram of P+2 bins. Each bin effectively provides an estimate of the probability o

91、f encountering the corresponding pattern in the texture</p><p>　　Variance measure has a continuous-valued output; hence, quantization of its feature space is needed. This was done by adding together feature

92、 distributions for every single model image in a total distribution, which was divided into B bins having an equal number of entries. Hence, the cut values of the bins of the histograms corresponded to the (100=B) percen

93、tile of the combined data. Deriving the cut values from the total distribution and allocating every bin the same amount of the combined da</p><p>　　2.6 Multiresolution Analysis</p><p>　　We have

94、presented general rotation-invariant operators for characterizing the spatial pattern and the contrast of local image texture using a circularly symmetric neighbor set of P pixels placed on a circle of radius R. By alter

95、ing P and R,we can realize operators for any quantization of the angular space and for any spatial resolution. Multiresolution analysis can be accomplished by combining the information provided by multiple operators of v

96、arying (P;R). In this study, we perform straightforw</p><p><b>　　(14)</b></p><p>　　where N is the number of operators and and correspond to the sample and model histograms extracte

97、d with operator n（n=1，…，N）, respectively. This expression is based on the additivity property of the G statistic (13), i.e., the results of several G tests can be summed to yield a meaningful result. If X and Y are indep

98、endent random events and ，， and are the respective marginal distributions for S and M, then </p><p><b>　　[5]</b></p><p>　　Generally, the assumption of independence between different

99、 texture features does not hold. However, estimation of exact joint probabilities is not feasible due to statistical unreliability and computational complexity of large multidimensional histograms. For example, the joint

100、 histogram of ，and would contain 4,680（10×18×26）cells. To satisfy the rule of thumb for statistical reliability, i.e., at least 10 entries per cell on average, the image should be of roughly （216+2R）(216+2R)

101、pixels in s</p><p>　　We have recently successfully employed this approach also in texture segmentation, where we quantitatively compared different alternatives for combining individual histograms for multire

102、solution analysis [6]. In this study, we restrict ourselves to combinations of at most three operators.</p><p>　　REFERENCES：</p><p>　　T. Ojala, K. Valkealahti, E. Oja, and M. PietikaÈinen,

103、“Texture Discrimination with Multi-Dimensional Distributions of Signed Gray Level Differences,” Pattern Recognition, vol. 34, pp. 727- 739, 2001.</p><p>　　T. Ojala, M. PietikaÈinen, and D. Harwood, “A C

104、omparative Study of Texture Measures with Classification Based on Feature Distributions,” Pattern Recognition, vol. 29, pp. 51-59, 1996.</p><p>　　M. PietikaÈinen, T. Ojala, and Z. Xu, “Rotation-Invarian