The FCRN neural network can be used to interpret depth maps on single-lens camera images. But how can we further improve the depth maps based on the intial photo?

Published by **Philipp Matthes** 6 months, 2 weeks ago

The FCRN depth prediction core ml model can be used to interpret depth information on monocular camera images. This is really useful, because it makes portrait effects available also for devices without a multi camera array, such as the iPhone SE or the iPhone 8. However, the output of the neural network isn’t as clear and precise as the disparity maps coming from a multi-camera array. It includes many artifacts from the neural processing. Here is an example of a generated depth map:

As you can see, the generated depth map is very rough and not really usable in this state. But we can make use of image postprocessing to further improve the looks of the depth map. Firstly, we could use a simple Gaussian blur filter over the depth map to further smoothen it. This would look something like this:

The Gaussian blur removes most of the artifacts, but has a severe downside which makes it almost useless for many kinds of applications. It also blurs all of the edges in the depth image. So how can we blur the image’s surfaces without losing the sharp edges?

We can use a simple image postprocessing technique called bilateral filtering (check the Wikipedia site) to preserve the edges while blurring. The output of bilateral filtering on our example image looks like this (right side):

You can see that the bilateral filtering really improves our depth map. It not only smoothes the grainy surfaces, but actually reintroduces edges into the depth map, which weren’t there before. To achieve this, we need to compute the blur weight for the depth map according to the diffuse maps change in pixel values (“delta”). If the change in pixel values of the photo is really high, we should smooth the depth map less to preserve edges. Vice versa, if the change in pixel values is comparatively small (e.g. on surfaces) we blur the depth map to further smoothen out artifacts from the depth map generation.

First of all, you need to generate the depth map as a `CGImage`

from the original image. Download the FCRN model (from the CoreML models page) and include it into your Xcode project. Then the inference can be performed as follows:

import Vision // TODO: Avoid force tries, avoid force unwraps // + implement proper error handling let image = UIImage(named: "test")! let model = try! VNCoreMLModel(for: FCRN().model) let cgImage = image.cgImage! var result: MLMultiArray? // NOTE: For simplicity, we perform the inference synchronously. // TODO: Link a proper inference handler and do not use dispatch groups. let dispatchGroup = DispatchGroup() dispatchGroup.enter() let request = VNCoreMLRequest(model: model) { request, error in guard error == nil, let observations = request.results as? [VNCoreMLFeatureValueObservation], let value = observations.first?.featureValue.multiArrayValue else { fatalError() } result = value dispatchGroup.leave() } request.imageCropAndScaleOption = .scaleFill try! VNImageRequestHandler( cgImage: cgImage, options: [:] ).perform([request]) dispatchGroup.wait()

This performs the inference using the CoreML model, synchronously using DispatchGroup. The `result`

will be a `MLMultiArray`

, which needs to be converted to a `CGImage`

now. Its up to you, how you perform this step, but I used **CoreMLHelpers** by Matthijs Hollemans for this:

var minValue: Double = .greatestFiniteMagnitude var maxValue: Double = 0 for i in 0 ..< 128 /* FCRN Output Height */ { for j in 0 ..< 160 /* FCRN Output Width */ { let index = i * 128 + j let value = array[index].doubleValue minValue = min(minValue, value) maxValue = max(maxValue, value) } } // This inverts the depth map and creates a CGImage using CoreMLHelpers // Website: https://github.com/hollance/CoreMLHelpers let depthCGImage: CGImage = array.cgImage(min: maxValue, max: minValue)!

The `CGImage`

depth map can now be used for the actual postprocessing. We are going to do this as follows:

let filter = BilateralFilter( diffuse: CIImage(cgImage: cgImage), depth: CIImage(cgImage: depthCGImage), sigmaR: 20, sigmaS: 0.05 ) let outputCIImage = filter.outputImage! let context = CIContext() let outputCGImage = context.createCGImage( outputCIImage, from: outputCIImage.extent )! // The final processed depth map let outputImage = UIImage(cgImage: outputCGImage)

This actual filter implementation is hidden behind `BilateralFilter`

. The `CIImage`

filter can be implemented as follows:

import CoreImage class BilateralFilter: CIFilter { private var diffuse: CIImage private var depth: CIImage private var sigmaR: NSNumber private var sigmaS: NSNumber init( diffuse: CIImage, depth: CIImage, sigmaR: NSNumber = 15, sigmaS: NSNumber = 0.2 ) { self.diffuse = diffuse self.depth = depth self.sigmaR = sigmaR self.sigmaS = sigmaS super.init() } required init?(coder: NSCoder) { fatalError() } private lazy var kernel: CIKernel = { () -> CIKernel in guard let filterPath = Bundle.main.path( forResource: "BilateralFilter", ofType: "cikernel" ), let filterContents = try? String(contentsOfFile: filterPath), let kernel = CIKernel(source: filterContents) else { fatalError("Bilateral Filter could not be built!") } return kernel }() override var outputImage: CIImage? { get { let rangeOfInterestCallback = { (index: Int32, rect: CGRect) -> CGRect in rect.insetBy( dx: CGFloat(-self.sigmaR.floatValue), dy: CGFloat(-self.sigmaR.floatValue) ) } let arguments = [ CISampler(image: diffuse), CISampler(image: depth), sigmaR, sigmaS ] return kernel.apply( extent: diffuse.extent, roiCallback: rangeOfInterestCallback, arguments: arguments ) } } }

Now, for the last step, we need to create a new shader under the filename `BilateralFilter.cikernel`

. Our shader will use the Core Image Kernel Language. The shader itself looks like this:

// The sample size of the kernel #define SAMPLE_SIZE 25 // Inverse square root of pi times 2 #define INV_SQRT_PI_2 0.39894 // Compute the normal probability distribution on a float value. float normpdf(float x, float sigma) { return INV_SQRT_PI_2 * exp(-0.5 * x * x / (sigma * sigma)) / sigma; } // Compute the normal probability distribution on a 3-dimensional vector. float normpdf3(vec3 v, float sigma) { return INV_SQRT_PI_2 * exp(-0.5 * dot(v, v) / (sigma * sigma)) / sigma; } // Blur the input depth image but preserve edges from the diffuse map. kernel vec4 BilateralFilter( sampler diffuse, sampler depth, float sigmaR, // Range float sigmaS // Spacial ) { // Create the one-dimensional sample kernel. Note that for // real-time rendering applications the kernel should be // precomputed for better rendering efficiency const int sampleKernelSize = (SAMPLE_SIZE - 1) / 2; float sampleKernel[SAMPLE_SIZE]; for (int i = 0; i <= sampleKernelSize; ++i) { float sampleKernelValue = normpdf(float(i), sigmaR); sampleKernel[sampleKernelSize + i] = sampleKernelValue; sampleKernel[sampleKernelSize - i] = sampleKernelValue; } // Normalization factor float Z = 0.0; // Spacial weight base reference float bZ = 1.0 / normpdf(0.0, sigmaS); // The destination of the current pixel in working space coordinates vec2 dWorkspace = destCoord(); // The diffuse and depth values of the target pixel vec3 targetDiffusePixel = sample(diffuse, samplerCoord(diffuse)).rgb; // The final rgb color which is going to be summed up vec3 finalColorRGB = vec3(0.0); for (int x = -sampleKernelSize; x <= sampleKernelSize; ++x) { for (int y = -sampleKernelSize; y <= sampleKernelSize; ++y) { // Sample the current partial kernel pixel of the diffuse map vec2 workingSpaceSampleCoordinate = dWorkspace + vec2(x, y); vec2 imageSpaceSampleCoordinate = samplerTransform(diffuse, workingSpaceSampleCoordinate); vec3 sampleDiffusePixel = sample(diffuse, imageSpaceSampleCoordinate).rgb; vec3 sampleDepthPixel = sample(depth, imageSpaceSampleCoordinate).rgb; vec3 delta = sampleDiffusePixel - targetDiffusePixel; float factor = normpdf3(delta, sigmaS) * bZ * sampleKernel[sampleKernelSize + x] * sampleKernel[sampleKernelSize + y]; Z += factor; finalColorRGB += factor * sampleDepthPixel; } } return vec4(finalColorRGB / Z, 1.0); }

That’s it! Once having created these two additional files, the shader should be successfully loaded by the custom `CIFilter`

.

The depth map can not only be further improved by bilateral filtering, but also with image segmentation. This is a topic which I will further investigate in the following weeks.

- The initial idea to use a bilateral filter was mentioned by Wei Liu et al. in “An efficient depth map preprocessing method based on structure-aided domain transform smoothing for 3D view generation” - https://doi.org/10.1371/journal.pone.0175910
- CoreMLHelpers by Matthijs Hollemans
- Thanks to the contributors of MetalPetal/SurfaceBlur and notjosh/NTJBilateralCIFilter for references on how the filter may be implemented. I adapted some of the princpiples but in the end completely built the filter and the shader by myself.

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