Principle and Implementation of object detection (III)

Target Detection Based on Hof Forest

In the previous section, we talked about the HOF transform (HT) and the generalized Hof transform (ght). Today we will continue with the Generalized Hof transformation. In the generalized Hof transformation, each voting element (such as the vertex in the edge pixel) accumulates the voting weights in the Hoff space. The voting weights of each element do not affect each other, this assumes that each pixel in the image space is independent, but is it true? Answer: No, especially when we participate in part-based voting today, this idea of independent voting elements is even more difficult. We have learned the probability graph model (Probabilistic graphic model) we all know that the graph model has a V structure, as shown in Figure 1:

(Figure 1)

X1, x2 is the voting element, and Y is the voting element in the Hoff space. Suppose that when we observe Y, or when we specify y, we observe the target in the image space, if X1 and X2 are generated by the target, are X1 and X2 independent? Obviously not, these elements should vote for y with a higher weight, while other elements cast a smaller weight (Figure 1 also shows that when given y = 1, X1, the probability of X2 increases by 0.25 from 0.33 ). This is the explain away question raised by Judea peal (even if two hidden causes are
Independent in the prior, they can become dependent when we observe an effect that they can both influence ). Since there is a ready-made framework: probability graph model, or strictly speaking probability model, we can improve generalized Hov voting to enter the probability space.

Let's talk about HUF forest. HUF forest was published on cvpr in 2009 by Juergen gall. By constructing a random forest, the image block (patch appearance) is directly mapped to the target center of gravity and the target center of gravity is found, other practices also involve building codebooks as voting elements. No matter what method we use, we can look at them as voting elements in the image space in the image Hof transformation, and then go to the HOF space to find the peak point to detect the target. Don't forget that today's topic is to enter the probability space for voting. Let's take a look at how the author enters the probability space. The author builds a random forest model. Random forest consists of N decision trees, which are independent of each other to classify the target, the number of n categories determines the target category. The training sample for each decision tree is

Where I is a local image block (patch) of the target, C is its class label (1 indicates the target, 0 indicates the background ), d indicates the offset vector (2D) from the image block in the bouding box to the Target Center, which plays a major role in the voting of the Target center of gravity; the purpose of a random tree growth is to minimize the nonpurity of the node sample type and offset, as shown in formula (2) and (3) in Figure 2:

(Figure 2)

The splitting criterion on the node uses the pixel value comparison method, and completes the decision tree construction through alternating minimization (Formula 1.

(Formula 1)

The leaf node records two important information items: CL indicates the positive sample ratio and DL sample offset. The two items (positive sample ratio and offset vector) are the voting elements. In addition, during the training, the author also adopted a cascade approach. Forest = 5 trees + 5 trees + 5 trees, that is, after the first five trees have been grown, some samples that are difficult to classify are then used to train the next batch of trees. In the detection phase, the patch is extracted from the image, and then the decision tree in the random forest is used for processing. Then, the voting is conducted in the HOV space to perform intensive block sampling on the image, finally, output the HOV image. But again, where is the probability space reflected? The key point is how to vote. If E (x) indicates a random event with the target center of gravity at the position X, it indicates the probability that the target center of gravity is at the position X when an image block is given, using Bayesian formulas and some equivalent replacements, this probability can be decomposed as shown in (formula 2:

(Formula 2)

(Formula 2) There are two items in the last line. The first item can be estimated using the pazen Window Based on the DL of the decision tree leaf node, and the second item is calculated directly using the CL of the leaf node. In this way (formula 2) can be converted to (Formula 3 ):

(Formula 3)

However (Formula 3) is only the probability of a decision tree. It is used as a random forest to calculate the average probability of all decision trees, as shown in formula 4:

(Formula 4)

In this way, a patch is used to vote for the center of gravity of the target near it in the probability space, and the voting of all patches is accumulated, as shown in formula 5:

(Formula 5)

The detection result is shown in Figure 3. However, if the center of gravity is detected, the target cannot be strictly framed. The target at different scales must be differentiated, in other words, we need to add a scale parameter. If we still want to consider the aspect ratio of the bounding box, we will add a parameter, but the calculation will also increase exponentially as the parameter increases.

(Figure 3)

Finally, let's take a look at the composition of the patch. The patch components used in the experiment are: 3 channels were used (intensity, absolute valueof X-and y-derivatives). The experiment results are good, however, the disadvantages are also described above. The implementation code Juergen gall homepage has been displayed. For more details, see references. Although Hov forest entered the probability space for voting, after all, it was calculated from the random forest. The probability of Hoff voting depends on the probability obtained by the random forest, in addition, there is no bidirectional causal reasoning between the voting element and the target. This is his flaw. Combined with the probability graph model, we can better combine the Hoff Voting Theory in the probability space, in addition, we can reduce the coupling degree with the random forest so that it can be extended to any probability acquisition method. Therefore, we intend to extend the Target Detection Based on the Hoff vote.

References:

Class-specific Hough forests for objectdetection. Juergen gall

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