Research on image processing algorithm of immune colloidal gold test paper detection

3.2.1. Improvement of weak classifier training algorithm

The training process of weak classifier is to calculate the eigenvalues of all training samples for each feature ($r$),and select a threshold ($\theta$) from the threshold candidate set.Under different bias ($p$),the classification error ($\epsilon$) of the corresponding weak classifier $g\left(x,f,p,\theta \right)$ is minimized. There are two sources of classification errors, namely:

(A) Error caused by misjudgment of quality control line or detection line as non-quality control line or non-detection line.

(B) Error caused by misjudgment of non-quality control line or non-detection line as quality control line or detection line.

Therefore, the classification error can be divided into two parts:

(A) The sum of the weight of the wrong samples of the quality control line or the detection line which is not the quality control line or the detection line:

(B) Misjudge the non-quality control line or non-detection line as the sum of the weight of the wrong samples of the quality control line or detection line:

Among them, ${\omega }_i$ is the weight of the $i$-th sample, $IA\left(x\right)$ is the indicative function, when $x\notin A$ is 1, when $x\notin A$ is 0.

The current AdaBoost algorithm treats the above two kinds of decision errors equally, but in the pictures collected by the colloidal gold detection device, generally the quality control line and detection line occupy a relatively small area, while the background area is relatively large, so the detection of quality control line and detection line in the image can be regarded as a small probability event, so the probability of class an error is greater than that of class B error Rate. In addition, in the process of strong classifier cascade, only through all strong classifiers can it be judged as quality control line or detection line. That is to say, if a target area, that is, the area of quality control line or detection line, is misjudged as a blank area, that is, the area of nonquality control line or detection line, this area will be excluded forever, and this error can’t be remedied. However, if the blank area is misjudged as the target area in a strong classifier, it is likely to be excluded by a strong classifier at a later level, which shows that this error can be remedied.

In view of the above situation, the training algorithm of weak classifier used in this paper is as follows for $j=$1, 2, 3,…, $m$ and $m$ is the total number of features:

(1) The eigenvalues of each sample are calculated by the eigenvalue $j$, and these eigenvalues are sorted.

(2) Given a constant $K$, its value range is 0 $<K<$ 1.

(3) Calculate the weight and $T^{+}$ of all positive samples (quality control line and detection line), and the weight and $T^{-}$ of all negative samples (non-quality control line and detection line); for and $i=$0, 1, 2,…, $n$ and $n$ is the total number of training samples.

Calculate the weight as$S_{j,i}^{+}$of the positive sample before the sample, and the weight as $S_{j,i}^{-}$ of the negative sample before the sample.

Calculating: ${\epsilon }_{j,i}=\min \left(k*S_{j,i}^{+}+\left(T^{-}-S_{j,i}^{-}\right),S_{j,i}^{-}+k*\left(T^{+}-S_{j,i}^{+}\right)\right).$

(4) Calculating: ${\epsilon }_j=\min \left\{{\epsilon }_{j,i}\right\}=\min \left\{\min \left(k*S_{j,i}^{+}+\left(T^{-}-S_{j,i}^{-}\right),S_{j,i}^{-}+k*\left(T^{+}-S_{j,i}^{+}\right)\right)\right\}.$

Record $p$ and $\theta$ at this time.

(5) Calculate the minimum classification error rate ε, and determine the threshold value $\theta$ and direction sign p of the weak classifier:

It can be seen from the above algorithm that the two cases of classification error are handled separately, which increases the attention to the class an error situation and more conforms to the fact that the target area detects small probability events. To apply the method of training weak classifier to the training process of strong classifier, only the calculation of the classification error of the best weak classifier needs to be changed into the following formula:

Other processes remain the same.

3.2.2. Improvement of sample weight updating rule

If the current weak classifier $g_t\left(x\right)$, a training sample $x_i$ is not classified correctly, that $g_t\left(x_i\right)=$ 1, $y_i=$ –1 or $g_t\left(x_i\right)=$ –1, $y_i=$ 1, that is $y_i{g}_t\left(x_i\right)=$–1, then there are:

and ${\alpha }_t=\frac{1}{2}\ln \left(\frac{1-{\epsilon }_t}{{\epsilon }_t}\right)\left({\epsilon }_t<\frac{1}{2}\right)$, $\exp \left({\alpha }_t\right)>$ 1, don’t consider the normalization factor $Z_t$, ${\omega }_{t+1,i}>{\omega }_{t,i}$.

If the current weak classifier $g_t\left(x\right)$ classifies a training sample $x_i$ correctly, then $g_t\left(x_i\right)=$ –1, $y_i=$ –1 or $g_t\left(x_i\right)=$1, $y_i=$1, that is, $y_i*g_t\left(x_i\right)=$ 1, then there are:

and ${\alpha }_t=\frac{1}{2}\ln \left(\frac{1-{\epsilon }_t}{{\epsilon }_t}\right)\left({\epsilon }_t<\frac{1}{2}\right)\text{,}$$\exp \left({\alpha }_t\right)>1\text{,}$ don’t consider the normalization factor $Z_t\text{,}$${\omega }_{t+1,i}<{\omega }_{t,i}$.

The updating rule of sample weight of AdaBoost algorithm guarantees to focus on difficult samples, but its disadvantages are also obvious:

(1) When the training samples contain some difficult samples, AdaBoost algorithm is difficult to classify these samples correctly. AdaBoost algorithm will focus on analyzing the difficult samples, which will lead to a sharp increase in the weight of the samples, leading to the phenomenon of degradation.

(2) When the training samples contain some difficult samples, the weight of correctly classified samples decreases exponentially due to the weight normalization, and the performance of the algorithm decreases with the increase of the number of iterations.

This paper improves the AdaBoost algorithm’s weight update rule, that is, in each training, the average value $m$ and standard deviation $\sigma$ of the sample weight are calculated. When the deviation between the weight of the wrong sample and the average weight m is greater than 3$\sigma$, the weight is no longer increased. The specific algorithm is as follows:

(1) Given the training samples ($x_1$, $y_1$), ($x_2$, $y_2$),…, ($x_n$, $y_n$), where $y_i=$ +1, –1 represents the samples of quality control line and detection line (positive samples) and non-quality control line and detection line (negative samples), respectively, determine the weak classifier $g\left(x,f,p,\theta \right)$ and the number of iterations $T$ (that is, the number of weak classifiers);

(2) Initialize sample weight: $D_1=\left({\omega }_{11},{\omega }_{12},{\omega }_{13},\cdots {\omega }_{1i}\cdots ,{\omega }_{1n}\right)$, ${\omega }_{1i}=1/n$, $i=\mathrm{1,2},\cdots ,n$, where $n$ is the total number of training samples.

(3) For $t=$ 1:$T$.

(A) Using the weak classifier algorithm, calculate the weighted classification error, find the weak classifier corresponding to the minimum classification error, record $f$, $p$, $\theta$, which are respectively $f_t$, $p_t$, ${\theta }_t$. The classification error of this optimal weak classifier can be expressed as:

(B) Order $g_t\left(x\right)=g\left(x,f_t,p_t,{\theta }_t\right)$, where $f_t$, $p_t$, ${\theta }_t$ are the minimization factors of ${\epsilon }_t$.

(C) Order: ${\alpha }_t=\frac{1}{2}\ln \left(\frac{1-{\epsilon }_t}{{\epsilon }_t}\right).$

Calculate the average value $m$ and standard deviation $\sigma$ of the sample weight of the current round:

(D) Update sample weight:

where $Z_t={\sum }_{i=1}^n{\omega }_{t,i}\exp \left(-{\alpha }_t{y}_i{g}_t\left(x_i\right)\right)$ is the normalization factor.

(4) Get the final strong classifier $G\left(x\right)=sign\left({\sum }_{t=1}^T{\alpha }_t{g}_t\left(x\right)\right)$.