Normalized Cross-Correlation (NCC) 

• $R(x,y)$ is the correlation value at the point $(x,y)$.
• $T(i,j)$ is the pixel value in the template at position $(i,j)$.
• $\overline{T}$ is the mean of the pixel values in the template.
• $I(x+i,y+j)$ is the pixel value in the image at position $(x+i,y+j)$.
• ${\overline{I}}_{x,y}$ is the mean of the pixel values in the region of the image being compared with the template.

 Procedure for Template Matching 

• Calculate the mean of the template$\overline{T}$:

  $$\overline{T}=\frac{1}{mn}\sum _{i=0}^{m-1}\sum _{j=0}^{n-1}T(i,j)$$

  where m and n are the dimensions of the template.
• Calculate the mean of the image region${\overline{I}}_{x,y}$:

  $${\overline{I}}_{x,y}=\frac{1}{pq}\sum _{i=0}^{p-1}\sum _{j=0}^{q-1}I(x+i,y+j)$$

  where p and q are the dimensions of the region.
• Calculate the numerator of the NCC:

  $$\sum _{i=0}^{m-1}\sum _{j=0}^{n-1}(T(i,j)-\overline{T})(I(x+i,y+j)-{\overline{I}}_{x,y})$$
• Calculate the denominator of the NCC:

  $$\sqrt{{\sum }_{i=0}^{m-1}{\sum }_{j=0}^{n-1}{(T(i,j)-\overline{T})}^2{\sum }_{i=0}^{m-1}{\sum }_{j=0}^{n-1}{(I(x+i,y+j)-{\overline{I}}_{x,y})}^2}$$
• Calculate the correlation value $R(x,y)$ for each position $(x,y)$ in the image.

4.

Non-maximum Suppression (NMS): the algorithm removes redundant bounding boxes using non-maximum suppression, ensuring only the most relevant boxes are considered. Modern object detectors usually follow a three-step recipe:

• proposing a search space of windows (exhaustive by sliding window or sparser using proposals)
• scoring/refining the window with a classifier/regressor,
• merging the bounding boxes around each detected object into a single best representative box.

This last stage is commonly referred to as “non-maximum suppression” and is a crucial step in pattern-matching algorithms to refine the detected object locations and eliminate redundant matches. NMS can be used to find distinctive feature points in an image. To improve the repeatability of a detected corner across multiple images, the corner is often selected as a local maximum whose cornerness is significantly higher than the close-by second-highest peak [19]. NMS with a small neighborhood size can produce an oversupply of initial peaks. These peaks are then compared with other peaks in a larger neighborhood to retain strong ones only. The initial peaks can be sorted during NMS to facilitate the later pruning step.

For some applications such as multi-view image matching, an evenly distributed set of interest points for matching is desirable. An oversupplied set of NMS point features can be given to an adaptive non-maximal suppression process [6], which reduces cluttered corners to improve their spatial distribution.

Consider a similarity score matrix $R(u,v)$ obtained after template matching, where u and v represent the coordinates of the image. Each element $R(u,v)$ denotes the similarity score at the corresponding location in the image. The non-maximum suppression algorithm $R_{nms}$ can be described as follows

$$\begin{array}{cc}\hfill & \left\{\begin{array}{cc}R(u,v)\hfill & \mathrm{if}R(u,v)\ge R(u\pm 1,v\pm 1)\mathrm{and}R(u,v)\ge R(u\pm 1,v)\mathrm{and}\hfill \\ & R(u,v)\ge R(u,v\pm 1)\hfill \\ 0\hfill & \mathrm{otherwise}\hfill \end{array}\right.\hfill \\ \hfill \end{array}$$

(1)

In this formulation:

• $R_{nms}$ represents the resulting score after non-maximum suppression.
• For each pixel location $(u,v)$ the algorithm checks whether the similarity score at that location is greater than or equal to the scores of its neighboring pixels in all eight directions (i.e., top-left, top, top-right, left, right, bottom-left, bottom, bottom-right).
• If the similarity score at $(u,v)$ is greater than or equal to the scores of all its neighbors, it is retained as a local maximum and assigned the same value.
• Otherwise, if $R(u,v)$ is not a local maximum, it is suppressed by setting its value to zero.

This process ensures that only the highest-scoring pixel in each local neighbourhood is retained, effectively removing redundant detections, and preserving only the most salient object instances in the image. By employing non-maximum suppression, pattern-matching algorithms can produce more accurate and concise results, facilitating precise object localization and recognition within complex visual scenes.

5.

Result Visualization: The final result was displayed, indicating the detected objects’ centres and their corresponding identification numbers (Figure 3).

Scale-Invariant Feature Transform (SIFT)

Oriented FAST and Rotated BRIEF (ORB)

 3.5. Haar Cascade Classifiers 

 4. Results and Discussion 

 4.5. Resource Consumption 

• Pattern Matching, SIFT, and ORB: Demonstrated efficient resource consumption, making them suitable for practical applications.
• Haar Cascade: Required significant computational resources during the training phase, with efficient resource consumption during detection. (requiring a large number of negative images and a few positive images)

The experimental analysis conducted in this study provides a detailed comparison of four distinct object detection algorithms: Pattern Matching, Haar Classifier, SIFT, and ORB. Each method was evaluated based on a set of performance metrics, including training time, detection time, total matches, precision, recall, and F1 score. The results provide valuable insights into the strengths and limitations of each technique, facilitating informed decisions for future applications in industrial automation and robotics.

The comparative analysis of the four algorithms—Pattern Matching, Haar Classifier, SIFT, and ORB—reveals distinct strengths and limitations across various performance metrics and computational aspects. The results are summarized in the Table 1.

Table 1. Results of Comparing Algorithms

Table 1. Results of Comparing Algorithms

	Training Time (hrs)	Latency (sec)	Total Matches	Precision	Recall	F1 Score
Pattern Matching	0	0.13	7	1.00	1.00	1.00
Haar Classifier	3.55	0.0951	7	1.00	1.00	1.00
SIFT	0	0.388	6	1.00	0.857	0.923
ORB	0	12.06	4	1.00	0.571	0.727

 Training Time 

• Pattern Matching, SIFT and ORB: These algorithms do not require training, making them advantageous in scenarios where rapid deployment is needed.
• Haar Classifier: Requires a substantial training time of 3.55 hours, indicating an initial setup cost. However, this investment pays off with excellent detection performance.

 Latency 

• Haar Classifier: The fastest detection time (0.0951 sec) highlights its efficiency post-training.
• Pattern Matching: Quick detection time (0.13 sec) without the need for training makes it a strong candidate for real-time applications.
• SIFT: Moderate detection time (0.388 sec) reflects its computational complexity due to the detailed feature extraction process.
• ORB: Surprisingly, ORB takes the longest detection time (12.06 sec), which is unexpected for a binary feature descriptor. This may be attributed to implementation details or the specific test conditions.

 Total Matches 

• Pattern Matching and Haar Classifier: Both achieve the highest number of matches (7), indicating high effectiveness in object detection.
• SIFT: Slightly lower total matches (6), reflecting its robustness but also its selective nature.
• ORB: The lowest total matches (4), highlighting potential limitations in detecting all relevant objects, especially in more complex scenes.

 Precision, Recall, and F1 Score 

• Precision: All four algorithms exhibit perfect precision (1.00), indicating that when they do make detections, they are consistently accurate.
• Recall: Pattern Matching and Haar Classifier achieve perfect recall (1.00), showing their ability to detect all relevant objects. SIFT has a slightly lower recall (0.857), while ORB has the lowest (0.571), indicating it misses more objects.
• F1 Score: The F1 Score combines precision and recall into a single metric. Pattern Matching and Haar Classifier both achieve the highest possible F1 score (1.00). SIFT has a respectable F1 score (0.923), while ORB lags behind at 0.727.

 5. Conclusions