How to calculate mAP for detection task for the PASCAL VOC Challenge?
To answer your questions:

Yes your approach is right
Of A, B and C the right answer is B.

The explanation is the following: In order to calculate Mean Average Precision (mAP) in the context of Object Detection you must compute the Average Precision (AP) for each class, and then compute the mean across all classes. The key here is to compute the AP for each class, in general for computing Precision (P) and Recall (R) you must define what are: True Positives (TP), False Positives (FP), True Negative (TN) and False Negative (FN). In the setting of Object Detection of the Pascal VOC Challenge are the following:

TP: are the Bounding Boxes (BB) that the intersection over union (IoU) with the ground truth (GT) is above 0.5
FP: two cases (a) BB that the IoU with GT is below 0.5 (b) the BB that have IoU with a GT that has already been detected.
TN: there are not true negative, the image are expected to contain at least one object
FN: those ground truthes for which the method failed to produce a BB

Now each predicted BB have a confidence value for the given class. So the scoring method sort the predictions for decreasing order of confidence and compute the P = TP / (TP + FP) and R = TP / (TP + FN) for each possible rank k = 1 up to the number of predictions. So now you have a (P, R) for each rank those P and R are the &quot;raw&quot; Precision-Recall curve. To compute the interpolated P-R curve foreach value of R you select the maximum P that has a corresponding R' &gt;= R.
There are two different ways to sample P-R curve points according to voc devkit doc.
For VOC Challenge before 2010, we select the maximum P obtained for any R' &gt;= R, which R belongs to 0, 0.1, ..., 1 (eleven points). The AP is then the average precision at each of the Recall thresholds. For VOC Challenge 2010 and after, we still select the maximum P for any R' &gt;= R, while R belongs to all unique recall values (include 0 and 1). The AP is then the area size under P-R curve. Notice that in the case that you don't have a value of P with Recall above some of the thresholds the Precision value is 0.
For instance consider the following output of a method given the class &quot;Aeroplane&quot;:
BB  | confidence | GT
----------------------
BB1 |  0.9       | 1
----------------------
BB2 |  0.9       | 1
----------------------
BB3 |  0.7       | 0
----------------------
BB4 |  0.7       | 0
----------------------
BB5 |  0.7       | 1
----------------------
BB6 |  0.7       | 0
----------------------
BB7 |  0.7       | 0
----------------------
BB8 |  0.7       | 1
----------------------
BB9 |  0.7       | 1
----------------------

Besides it not detected bounding boxes in two images, so we have FN = 2. The previous table is the ordered rank by confidence value of the predictions of the method GT = 1 means is a TP and GT = 0 FP. So TP=5 (BB1, BB2, BB5, BB8 and BB9), FP=5. For the case of rank=3 the precision drops because BB1 was already detected, so even if the object is indeed present it counts as a FP. .
rank=1  precision=1.00 and recall=0.14
----------
rank=2  precision=1.00 and recall=0.29
----------
rank=3  precision=0.66 and recall=0.29
----------
rank=4  precision=0.50 and recall=0.29
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rank=5  precision=0.40 and recall=0.29
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rank=6  precision=0.50 and recall=0.43
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rank=7  precision=0.43 and recall=0.43
----------
rank=8  precision=0.38 and recall=0.43
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rank=9  precision=0.44 and recall=0.57
----------
rank=10 precision=0.50 and recall=0.71
----------

Given the previous results:
If we used the way before voc2010, the interpolated Precision values are 1, 1, 1, 0.5, 0.5, 0.5, 0.5, 0.5, 0, 0, 0. Then AP = 5.5 / 11 = 0.5 for the class of &quot;Aeroplanes&quot;.
Else if we used the way since voc2010, the interpolated Precision values are 1, 1, 1, 0.5, 0.5, 0.5, 0 for seven unique recalls that are 0, 0.14, 0.29, 0.43, 0.57, 0.71, 1.Then AP = (0.14-0)*1 + (0.29-0.14)*1 + (0.43-0.29)*0.5 + (0.57-0.43)*0.5 + (0.71-0.57)*0.5 + (1-0.71)*0 = 0.5 for the class of &quot;Aeroplanes&quot;.
Repeat for each class and then you have the (mAP).
More information can be found in the following links 1, 2. Also you should check the paper: The PASCAL Visual Object Classes Challenge: A Retrospective for a more detailed explanation.