WPF: access UI element from another thread

Thread t = new Thread(new ThreadStart(DoPointsShift));
t.Start();

private void DoPointsShift()
        {
            int turnsPerMinute = 5;
            long delay = 60 / turnsPerMinute * 1000 / (360 / 2);
            long deltaDelay = delay;

        int beginTime = Environment.TickCount;
        EasingFunctionBase ease = new CircleEase();
        ease.EasingMode = EasingMode.EaseInOut;
        while (true)
        {
            TimeSpan duration = TimeSpan.FromSeconds(1 - 1 * rnd.NextDouble());
            foreach (var p in points)
            {
                var x = p.OriginX - 50 + rnd.NextDouble() * 100;
                var y = p.OriginY - 50 + rnd.NextDouble() * 100;
                PointAnimation anim = new PointAnimation(new Point(x, y), duration);
                anim.EasingFunction = ease;
                Dispatcher.BeginInvoke(new Action(() =>
                {
                    p.BeginAnimation(ParallaxPoint.PointCoordProperty, anim); //exception here
                }));
            }
            while (Environment.TickCount - beginTime < delay) { }
            delay += deltaDelay;
        }
    }