Test the performance of centroid tracker update method and understand its scaling with the number of objects

[himanshunaidu]

Currently, for a simple 2x2 old vs new object matrix, it takes less than 1 ms.
E.g. Centroid tracking time: 0.121333 ms

However, if we have numerous objects, say 100x100, this tracking time could blow up.
So we will have to check how to speed up the performance, and how to handle the edge case of having too many objects to compare between.

[himanshunaidu]

Bottleneck 1

Warping of old centroids

iOSPointMapper/IOSAccessAssessment/Segmentation/Helpers/CentroidTracker.swift

Lines 205 to 209 in b76fdf7

	private func warpedPoint(_ point: CGPoint, using warpTransform: simd_float3x3) -> CGPoint {
	let vector0 = SIMD3<Float>(x: Float(point.x), y: Float(point.y), z: 1)
	let vector1 = warpTransform * vector0
	return CGPoint(x: CGFloat(vector1.x / vector1.z), y: CGFloat(vector1.y / vector1.z))
	}

May want to use Metal instead for the transformation:

kernel void homographyWarpKernel(
    texture2d<float, access::read> inputTexture [[texture(0)]],
    texture2d<float, access::write> outputTexture [[texture(1)]],
    constant float3x3& inverseHomography [[buffer(0)]],
    uint2 gid [[thread_position_in_grid]])
{
    float2 outputCoord = float2(gid);
    float2 imageSize = float2(outputTexture.get_width(), outputTexture.get_height());
    
    float3 pos = float3(outputCoord, 1.0);
    float3 warped = inverseHomography * pos;
    float2 sampleUV = warped.xy / warped.z;
    
    float2 inputImageSize = float2(inputTexture.get_width(), inputTexture.get_height());
    float2 pixelCoord = sampleUV;

    float4 color = float4(pixelCoord.x, pixelCoord.y, 0.0, 1.0);

    if (all(pixelCoord >= float2(0.0)) && all(pixelCoord < inputImageSize)) {
        // Only read if inside bounds
        color = inputTexture.read(uint2(pixelCoord));
    }

    outputTexture.write(color, gid);
}

[himanshunaidu]

Bottleneck 2

Computing distance matrix and performing the matching.

iOSPointMapper/IOSAccessAssessment/Segmentation/Helpers/CentroidTracker.swift

Line 99 in b76fdf7

let distanceMatrix = computeDistanceMatrix(objects: objects, inputObjects: inputObjects);

... until end of update method

Need to figure out how to optimize this. Maybe on Metal.