How to upload picture and store to database in Laravel 5

I need to upload picture and store to database in Laravel 5.

My current code:

Form:

<form method="POST" enctype="multipart/form-data" action="">
    {!! csrf_field() !!}
    <div class="form-group">
        <label for="name">Name</label>
        <input type="text" name="name" id="name" class="form-control" required>
    </div>
    <div class="form-group">
        <label for="image">Image</label>
        <input type="file" id="image">
    </div>
    <div class="form-group">
        <button type="submit" class="btn btn-primary">Save</button>
    </div>
</form>

Controller:

public function store(Request $request)
{
    $this->validate($request, [
        'name' => 'required|max:100|unique:products',
    ]);

    $input = $request->all();
    Product::create($input);

    return redirect('products');
}

$request->hasFile('image')) returns false.

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